Answer
$-5,5,1$
Work Step by Step
Given: $x^3-x^2=25x-25$ or, $x^3-x^2-25x+25=0$
or, $x^2(x-1)-25(x-1)=0$
Need to use factorization to solve the quadratic equation.
This can be factorized as follows:
$(x^2-25)(x-1)=0$
or, $(x-5)(x+5)(x-1)=0 $
Set each factor equal to zero, we get
$x=-5,5,1$
