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Question 273112: solve: 2n(2n+4)=6n^2+9n
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 2n(2n+4)=6n^(2)+9n
Multiply 2n by each term inside the parentheses.
(4n^(2)+8n)=6n^(2)+9n
Remove the parentheses around the expression 4n^(2)+8n.
4n^(2)+8n=6n^(2)+9n
Move all terms not containing n to the right-hand side of the equation.
4n^(2)+8n-6n^(2)-9n=0
Since 4n^(2) and -6n^(2) are like terms, add -6n^(2) to 4n^(2) to get -2n^(2).
-2n^(2)+8n-9n=0
Since 8n and -9n are like terms, add -9n to 8n to get -n.
-2n^(2)-n=0
Multiply each term in the equation by -1.
2n^(2)+n=0
Factor out the GCF of n from each term in the polynomial.
n(2n)+n(1)=0
Factor out the GCF of n from 2n^(2)+n.
n(2n+1)=0
Set the single term factor on the left-hand side of the equation equal to 0.
n=0
Set each of the factors of the left-hand side of the equation equal to 0.
2n+1=0
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
2n=-1
Divide each term in the equation by 2.
(2n)/(2)=-(1)/(2)
Simplify the left-hand side of the equation by canceling the common terms.
n=-(1)/(2)
The complete solution is the set of the individual solutions.
n=0,-(1)/(2)
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