(x-4)(8x+64)=0

Solution for (x-4)(8x+64)=0 equation:

Simplifying
(x + -4)(8x + 64) = 0

Reorder the terms:
(-4 + x)(8x + 64) = 0

Reorder the terms:
(-4 + x)(64 + 8x) = 0

Multiply (-4 + x) * (64 + 8x)
(-4(64 + 8x) + x(64 + 8x)) = 0
((64 * -4 + 8x * -4) + x(64 + 8x)) = 0
((-256 + -32x) + x(64 + 8x)) = 0
(-256 + -32x + (64 * x + 8x * x)) = 0
(-256 + -32x + (64x + 8x2)) = 0

Combine like terms: -32x + 64x = 32x
(-256 + 32x + 8x2) = 0

Solving
-256 + 32x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-32 + 4x + x2) = 0

Factor a trinomial.
8((-8 + -1x)(4 + -1x)) = 0

Ignore the factor 8.
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 '(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
Solution
x = {-8, 4}