SOLUTION: Hi, I tried to solve for 5x^2=3x+2 and thought the answer is x=2/5 and x=-2. Also, I tried to solve 3x^3 +2x^2=x and came up with x=0, 1/3, -1. I am not sure of these answers.

Question 120450: Hi, I tried to solve for 5x^2=3x+2 and thought the answer is x=2/5 and x=-2.
Also, I tried to solve 3x^3 +2x^2=x and came up with x=0, 1/3, -1. I am not
sure of these answers. Can you please help me? Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Start with the given equation

Subtract 5x^2 from both sides.

Rearrange the terms.

Factor the right side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answer is
or

Notice if we graph we can see that the roots are and . So this visually verifies our answer.

#2

Start with the given equation

Subtract x from both sides.

Factor the left side

Now set each factor equal to zero:
, or

, or Now solve for x in each case

So our answer is
, or

Notice if we graph we can see that the roots are , and . So this visually verifies our answer.

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