(x-4)(x+4)(5)-(x+4)(x-2)(2)=(4)(x+4)

Solution for (x-4)(x+4)(5)-(x+4)(x-2)(2)=(4)(x+4) equation:

Simplifying
(x + -4)(x + 4)(5) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Reorder the terms:
(-4 + x)(x + 4)(5) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Reorder the terms:
(-4 + x)(4 + x)(5) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Reorder the terms for easier multiplication:
5(-4 + x)(4 + x) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Multiply (-4 + x) * (4 + x)
5(-4(4 + x) + x(4 + x)) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
5((4 * -4 + x * -4) + x(4 + x)) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
5((-16 + -4x) + x(4 + x)) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
5(-16 + -4x + (4 * x + x * x)) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
5(-16 + -4x + (4x + x2)) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Combine like terms: -4x + 4x = 0
5(-16 + 0 + x2) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
5(-16 + x2) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
(-16 * 5 + x2 * 5) + -1(x + 4)(x + -2)(2) = (4)(x + 4)
(-80 + 5x2) + -1(x + 4)(x + -2)(2) = (4)(x + 4)

Reorder the terms:
-80 + 5x2 + -1(4 + x)(x + -2)(2) = (4)(x + 4)

Reorder the terms:
-80 + 5x2 + -1(4 + x)(-2 + x)(2) = (4)(x + 4)

Reorder the terms for easier multiplication:
-80 + 5x2 + -1 * 2(4 + x)(-2 + x) = (4)(x + 4)

Multiply -1 * 2
-80 + 5x2 + -2(4 + x)(-2 + x) = (4)(x + 4)

Multiply (4 + x) * (-2 + x)
-80 + 5x2 + -2(4(-2 + x) + x(-2 + x)) = (4)(x + 4)
-80 + 5x2 + -2((-2 * 4 + x * 4) + x(-2 + x)) = (4)(x + 4)
-80 + 5x2 + -2((-8 + 4x) + x(-2 + x)) = (4)(x + 4)
-80 + 5x2 + -2(-8 + 4x + (-2 * x + x * x)) = (4)(x + 4)
-80 + 5x2 + -2(-8 + 4x + (-2x + x2)) = (4)(x + 4)

Combine like terms: 4x + -2x = 2x
-80 + 5x2 + -2(-8 + 2x + x2) = (4)(x + 4)
-80 + 5x2 + (-8 * -2 + 2x * -2 + x2 * -2) = (4)(x + 4)
-80 + 5x2 + (16 + -4x + -2x2) = (4)(x + 4)

Reorder the terms:
-80 + 16 + -4x + 5x2 + -2x2 = (4)(x + 4)

Combine like terms: -80 + 16 = -64
-64 + -4x + 5x2 + -2x2 = (4)(x + 4)

Combine like terms: 5x2 + -2x2 = 3x2
-64 + -4x + 3x2 = (4)(x + 4)

Reorder the terms:
-64 + -4x + 3x2 = 4(4 + x)
-64 + -4x + 3x2 = (4 * 4 + x * 4)
-64 + -4x + 3x2 = (16 + 4x)

Solving
-64 + -4x + 3x2 = 16 + 4x

Solving for variable 'x'.

Reorder the terms:
-64 + -16 + -4x + -4x + 3x2 = 16 + 4x + -16 + -4x

Combine like terms: -64 + -16 = -80
-80 + -4x + -4x + 3x2 = 16 + 4x + -16 + -4x

Combine like terms: -4x + -4x = -8x
-80 + -8x + 3x2 = 16 + 4x + -16 + -4x

Reorder the terms:
-80 + -8x + 3x2 = 16 + -16 + 4x + -4x

Combine like terms: 16 + -16 = 0
-80 + -8x + 3x2 = 0 + 4x + -4x
-80 + -8x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-80 + -8x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(20 + -3x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(20 + -3x)' equal to zero and attempt to solve:

Simplifying
20 + -3x = 0

Solving
20 + -3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3x = 0 + -20
-3x = 0 + -20

Combine like terms: 0 + -20 = -20
-3x = -20

Divide each side by '-3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {-4, 6.666666667}