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

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


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

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

Reorder the terms for easier multiplication:
2(4 + x) = (x + 4)(x + 4)
(4 * 2 + x * 2) = (x + 4)(x + 4)
(8 + 2x) = (x + 4)(x + 4)

Reorder the terms:
8 + 2x = (4 + x)(x + 4)

Reorder the terms:
8 + 2x = (4 + x)(4 + x)

Multiply (4 + x) * (4 + x)
8 + 2x = (4(4 + x) + x(4 + x))
8 + 2x = ((4 * 4 + x * 4) + x(4 + x))
8 + 2x = ((16 + 4x) + x(4 + x))
8 + 2x = (16 + 4x + (4 * x + x * x))
8 + 2x = (16 + 4x + (4x + x2))

Combine like terms: 4x + 4x = 8x
8 + 2x = (16 + 8x + x2)

Solving
8 + 2x = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -16 + 2x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 8 + -16 = -8
-8 + 2x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 2x + -8x = -6x
-8 + -6x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
-8 + -6x + -1x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-8 + -6x + -1x2 = 0 + 8x + -8x + x2 + -1x2
-8 + -6x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-8 + -6x + -1x2 = 0 + x2 + -1x2
-8 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 6x + x2) = 0

Factor a trinomial.
-1((4 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4

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 = {-4, -2}

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