x(x-1)+(x-1)(x+2)=0

Solution for x(x-1)+(x-1)(x+2)=0 equation:

Simplifying
x(x + -1) + (x + -1)(x + 2) = 0

Reorder the terms:
x(-1 + x) + (x + -1)(x + 2) = 0
(-1 * x + x * x) + (x + -1)(x + 2) = 0
(-1x + x2) + (x + -1)(x + 2) = 0

Reorder the terms:
-1x + x2 + (-1 + x)(x + 2) = 0

Reorder the terms:
-1x + x2 + (-1 + x)(2 + x) = 0

Multiply (-1 + x) * (2 + x)
-1x + x2 + (-1(2 + x) + x(2 + x)) = 0
-1x + x2 + ((2 * -1 + x * -1) + x(2 + x)) = 0
-1x + x2 + ((-2 + -1x) + x(2 + x)) = 0
-1x + x2 + (-2 + -1x + (2 * x + x * x)) = 0
-1x + x2 + (-2 + -1x + (2x + x2)) = 0

Combine like terms: -1x + 2x = 1x
-1x + x2 + (-2 + 1x + x2) = 0

Reorder the terms:
-2 + -1x + 1x + x2 + x2 = 0

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

Combine like terms: x2 + x2 = 2x2
-2 + 2x2 = 0

Solving
-2 + 2x2 = 0

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + 2x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2x2 = 0 + 2
2x2 = 0 + 2

Combine like terms: 0 + 2 = 2
2x2 = 2

Divide each side by '2'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}