(x-4)(x-4)(5)=500

Solution for (x-4)(x-4)(5)=500 equation:

Simplifying
(x + -4)(x + -4)(5) = 500

Reorder the terms:
(-4 + x)(x + -4)(5) = 500

Reorder the terms:
(-4 + x)(-4 + x)(5) = 500

Reorder the terms for easier multiplication:
5(-4 + x)(-4 + x) = 500

Multiply (-4 + x) * (-4 + x)
5(-4(-4 + x) + x(-4 + x)) = 500
5((-4 * -4 + x * -4) + x(-4 + x)) = 500
5((16 + -4x) + x(-4 + x)) = 500
5(16 + -4x + (-4 * x + x * x)) = 500
5(16 + -4x + (-4x + x2)) = 500

Combine like terms: -4x + -4x = -8x
5(16 + -8x + x2) = 500
(16 * 5 + -8x * 5 + x2 * 5) = 500
(80 + -40x + 5x2) = 500

Solving
80 + -40x + 5x2 = 500

Solving for variable 'x'.

Reorder the terms:
80 + -500 + -40x + 5x2 = 500 + -500

Combine like terms: 80 + -500 = -420
-420 + -40x + 5x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-420 + -40x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-84 + -8x + x2) = 0

Factor a trinomial.
5((-6 + -1x)(14 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-6, 14}