2x+4=(2x+2)(x+2)

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


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

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

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

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

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

Combine like terms: 2x + 4x = 6x
4 + 2x = (4 + 6x + 2x2)

Add '-4' to each side of the equation.
4 + -4 + 2x = 4 + 6x + -4 + 2x2

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

Reorder the terms:
2x = 4 + -4 + 6x + 2x2

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

Solving
2x = 6x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
-4x + -2x2 = 6x + -6x + 2x2 + -2x2

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

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

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

Ignore the factor -2.

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 '(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
Solution
x = {0, -2}

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