(x-2)(2x+2)=(x+4)(x-1)

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Solution for (x-2)(2x+2)=(x+4)(x-1) equation: 


Simplifying
(x + -2)(2x + 2) = (x + 4)(x + -1)

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

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

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

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

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

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

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

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

Add '4' to each side of the equation.
-4 + -2x + 4 + 2x2 = -4 + 3x + 4 + x2

Reorder the terms:
-4 + 4 + -2x + 2x2 = -4 + 3x + 4 + x2

Combine like terms: -4 + 4 = 0
0 + -2x + 2x2 = -4 + 3x + 4 + x2
-2x + 2x2 = -4 + 3x + 4 + x2

Reorder the terms:
-2x + 2x2 = -4 + 4 + 3x + x2

Combine like terms: -4 + 4 = 0
-2x + 2x2 = 0 + 3x + x2
-2x + 2x2 = 3x + x2

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

Solving for variable 'x'.

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

Combine like terms: -2x + -3x = -5x
-5x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-5x + 1x2 = 3x + x2 + -3x + -1x2

Reorder the terms:
-5x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-5x + 1x2 = 0 + x2 + -1x2
-5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, 5}

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