x^2-3(x-1)(x+2)=x

Solution for x^2-3(x-1)(x+2)=x equation:

Simplifying
x2 + -3(x + -1)(x + 2) = x

Reorder the terms:
x2 + -3(-1 + x)(x + 2) = x

Reorder the terms:
x2 + -3(-1 + x)(2 + x) = x

Multiply (-1 + x) * (2 + x)
x2 + -3(-1(2 + x) + x(2 + x)) = x
x2 + -3((2 * -1 + x * -1) + x(2 + x)) = x
x2 + -3((-2 + -1x) + x(2 + x)) = x
x2 + -3(-2 + -1x + (2 * x + x * x)) = x
x2 + -3(-2 + -1x + (2x + x2)) = x

Combine like terms: -1x + 2x = 1x
x2 + -3(-2 + 1x + x2) = x
x2 + (-2 * -3 + 1x * -3 + x2 * -3) = x
x2 + (6 + -3x + -3x2) = x

Reorder the terms:
6 + -3x + x2 + -3x2 = x

Combine like terms: x2 + -3x2 = -2x2
6 + -3x + -2x2 = x

Solving
6 + -3x + -2x2 = x

Solving for variable 'x'.

Reorder the terms:
6 + -3x + -1x + -2x2 = x + -1x

Combine like terms: -3x + -1x = -4x
6 + -4x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
6 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2x + -1x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}