x+16=(x-4)(x-4)

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Solution for x+16=(x-4)(x-4) equation: 


Simplifying
x + 16 = (x + -4)(x + -4)

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

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

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

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

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

Add '-16' to each side of the equation.
16 + -16 + x = 16 + -8x + -16 + x2

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

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

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

Solving
x = -8x + x2

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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