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

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


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

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

Reorder the terms for easier multiplication:
2(4 + x) = (4 + -1x)(4 + x)
(4 * 2 + x * 2) = (4 + -1x)(4 + x)
(8 + 2x) = (4 + -1x)(4 + x)

Multiply (4 + -1x) * (4 + x)
8 + 2x = (4(4 + x) + -1x * (4 + x))
8 + 2x = ((4 * 4 + x * 4) + -1x * (4 + x))
8 + 2x = ((16 + 4x) + -1x * (4 + x))
8 + 2x = (16 + 4x + (4 * -1x + x * -1x))
8 + 2x = (16 + 4x + (-4x + -1x2))

Combine like terms: 4x + -4x = 0
8 + 2x = (16 + 0 + -1x2)
8 + 2x = (16 + -1x2)

Solving
8 + 2x = 16 + -1x2

Solving for variable 'x'.

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

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

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

Combine like terms: 16 + -16 = 0
-8 + 2x + x2 = 0 + -1x2 + x2
-8 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-8 + 2x + x2 = 0

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


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}

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