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

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

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

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

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

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

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

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

Solving
4x + 2x2 = -2 + 1x + x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: -2 + 2 = 0
2 + 3x + 1x2 = 0 + 1x + -1x + x2 + -1x2
2 + 3x + 1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
2 + 3x + 1x2 = 0 + x2 + -1x2
2 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + 1x2 = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2, -1}