x+8=(x-4)(x-4)

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Solution for x+8=(x-4)(x-4) equation: 


Simplifying
x + 8 = (x + -4)(x + -4)

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

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

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

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

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

Solving
8 + x = 16 + -8x + x2

Solving for variable 'x'.

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

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

Combine like terms: x + 8x = 9x
-8 + 9x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Reorder the terms:
-8 + 9x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-8 + 9x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-8 + 9x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-8 + 9x + -1x2 = 0 + x2 + -1x2
-8 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + 9x + -1x2 = 0

Factor a trinomial.
(-8 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {8, 1}

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