SOLUTION: (3y+2)(y+3)=y+14

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Question 38527This question is from textbook
: (3y+2)(y+3)=y+14 This question is from textbook

Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=0.666666666666667,y=-4.
  • Graphical form: Equation %283y%2B2%29%2A%28y%2B3%29=y%2B14 was fully solved.
  • Text form: (3y+2)*(y+3)=y+14 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%283y%2B2%29%2A%28y%2B3%29=y%2B14+%29
    For tutors: simplify_cartoon( (3y+2)*(y+3)=y+14 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %283%2Ay%2B2%29%2A%28y%2B3%29=highlight_red%28+y%2B14+%29.
Moved these terms to the left highlight_green%28+-y+%29,highlight_green%28+-14+%29
It becomes %283%2Ay%2B2%29%2A%28y%2B3%29-highlight_green%28+y+%29-highlight_green%28+14+%29=0.
Look at highlight_red%28+%283%2Ay%2B2%29%2A%28y%2B3%29+%29-y-14=0.
Expanded term %28y%2B3%29 by using associative property on %283%2Ay%2B2%29
It becomes highlight_green%28+%28y%2B3%29%2A3%2Ay+%29%2Bhighlight_green%28+%28y%2B3%29%2A2+%29-y-14=0.
Look at highlight_red%28+%28y%2B3%29%2A3%2Ay+%29%2B%28y%2B3%29%2A2-y-14=0.
Expanded term 3%2Ay by using associative property on %28y%2B3%29
It becomes highlight_green%28+3%2Ay%2Ay+%29%2Bhighlight_green%28+3%2Ay%2A3+%29%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ay%2Ay%2Bhighlight_red%28+3+%29%2Ay%2Ahighlight_red%28+3+%29%2B%28y%2B3%29%2A2-y-14=0.
Multiplied numerator integers
It becomes 3%2Ay%2Ay%2Bhighlight_green%28+9+%29%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ahighlight_red%28+y+%29%2Ahighlight_red%28+y+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E2+%29
It becomes 3%2Ahighlight_green%28+y%5E2+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+9%2Ay+%29%2B%28y%2B3%29%2A2-highlight_red%28+y+%29-14=0.
Eliminated similar terms highlight_red%28+9%2Ay+%29,highlight_red%28+-y+%29 replacing them with highlight_green%28+%289-1%29%2Ay+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+%289-1%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2B%28highlight_red%28+9+%29-highlight_red%28+1+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B%28highlight_green%28+8+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+8+%29%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+8+%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2Bhighlight_red%28+%28y%2B3%29%2A2+%29-14=0.
Expanded term 2 by using associative property on %28y%2B3%29
It becomes 3%2Ay%5E2%2B8%2Ay%2Bhighlight_green%28+2%2Ay+%29%2Bhighlight_green%28+2%2A3+%29-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+3+%29-14=0.
Multiplied numerator integers
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+6+%29-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+6+%29-highlight_red%28+14+%29=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+-8+%29=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+-8+%29=0.
Removed extra sign in front of -8
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay-highlight_green%28+8+%29=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+8%2Ay+%29%2Bhighlight_red%28+2%2Ay+%29-8=0.
Eliminated similar terms highlight_red%28+8%2Ay+%29,highlight_red%28+2%2Ay+%29 replacing them with highlight_green%28+%288%2B2%29%2Ay+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+%288%2B2%29%2Ay+%29-8=0.
Look at 3%2Ay%5E2%2B%28highlight_red%28+8+%29%2Bhighlight_red%28+2+%29%29%2Ay-8=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B%28highlight_green%28+10+%29%29%2Ay-8=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+10+%29%29%2Ay+%29-8=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+10+%29%2Ay-8=0.
Look at highlight_red%28+3%2Ay%5E2%2B10%2Ay-8+%29=0.
Equation highlight_red%28+3%2Ay%5E2%2B10%2Ay-8=0+%29 is a quadratic equation: 3*y^2+10*y-8 =0, and has solutions 0.666666666666667,-4
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=0.666666666666667,y=-4.

Universal Simplifier and Solver


Done!

Hope this helps!