SOLUTION: how to factor or get the zeros of x^2 = x^3

SOLUTION: how to factor or get the zeros of x^2 = x^3 - 6x Thank you

Question 1006368: how to factor or get the zeros of x^2 = x^3 - 6x
Thank you
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x^2 = x^3 -6x
combine terms and set = 0
x^3 - x^2 - 6x = 0
factor x out
x(x^2 -x -6) = 0
factor polynomial
x(x-3)(x+2) = 0
the zeros are x = 0, 3, -2
check the answers by substituting for x
********************************************************************************
0^2 = 0^3 - 6*0
0 = 0
**********************
3^2 = 3^3 - 6*3
9 = 27 - 18
9 = 9
***********************
(-2)^2 = (-2)^3 - 6*(-2)
4 = -8 + 12
4 = 4
*****************************************************************************
our answers check, here is a graph of the equation

note the values of x where the equation crosses the x axis

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