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

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


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

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

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

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

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

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

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

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

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

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

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

Multiply (-2 + x) * (2 + x)
-2 + -2x = (-2(2 + x) + x(2 + x)) + -1(x + -1) * 2
-2 + -2x = ((2 * -2 + x * -2) + x(2 + x)) + -1(x + -1) * 2
-2 + -2x = ((-4 + -2x) + x(2 + x)) + -1(x + -1) * 2
-2 + -2x = (-4 + -2x + (2 * x + x * x)) + -1(x + -1) * 2
-2 + -2x = (-4 + -2x + (2x + x2)) + -1(x + -1) * 2

Combine like terms: -2x + 2x = 0
-2 + -2x = (-4 + 0 + x2) + -1(x + -1) * 2
-2 + -2x = (-4 + x2) + -1(x + -1) * 2

Reorder the terms:
-2 + -2x = -4 + x2 + -1(-1 + x) * 2

Reorder the terms for easier multiplication:
-2 + -2x = -4 + x2 + -1 * 2(-1 + x)

Multiply -1 * 2
-2 + -2x = -4 + x2 + -2(-1 + x)
-2 + -2x = -4 + x2 + (-1 * -2 + x * -2)
-2 + -2x = -4 + x2 + (2 + -2x)

Reorder the terms:
-2 + -2x = -4 + 2 + -2x + x2

Combine like terms: -4 + 2 = -2
-2 + -2x = -2 + -2x + x2

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

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

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

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

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

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

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

Solving
0 = x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
0 + -1x2 = x2 + -1x2
Remove the zero:
-1x2 = x2 + -1x2

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

Divide each side by '-1'.
x2 = 0

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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