x^2+(x-8)(x-8)=320

Solution for x^2+(x-8)(x-8)=320 equation:

Simplifying
x2 + (x + -8)(x + -8) = 320

Reorder the terms:
x2 + (-8 + x)(x + -8) = 320

Reorder the terms:
x2 + (-8 + x)(-8 + x) = 320

Multiply (-8 + x) * (-8 + x)
x2 + (-8(-8 + x) + x(-8 + x)) = 320
x2 + ((-8 * -8 + x * -8) + x(-8 + x)) = 320
x2 + ((64 + -8x) + x(-8 + x)) = 320
x2 + (64 + -8x + (-8 * x + x * x)) = 320
x2 + (64 + -8x + (-8x + x2)) = 320

Combine like terms: -8x + -8x = -16x
x2 + (64 + -16x + x2) = 320

Reorder the terms:
64 + -16x + x2 + x2 = 320

Combine like terms: x2 + x2 = 2x2
64 + -16x + 2x2 = 320

Solving
64 + -16x + 2x2 = 320

Solving for variable 'x'.

Reorder the terms:
64 + -320 + -16x + 2x2 = 320 + -320

Combine like terms: 64 + -320 = -256
-256 + -16x + 2x2 = 320 + -320

Combine like terms: 320 + -320 = 0
-256 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-128 + -8x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(16 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-8, 16}