(x-4)1+8=(x-4)(x+4)1

Solution for (x-4)1+8=(x-4)(x+4)1 equation:

Simplifying
(x + -4) * 1 + 8 = (x + -4)(x + 4) * 1

Reorder the terms:
(-4 + x) * 1 + 8 = (x + -4)(x + 4) * 1

Reorder the terms for easier multiplication:
1(-4 + x) + 8 = (x + -4)(x + 4) * 1
(-4 * 1 + x * 1) + 8 = (x + -4)(x + 4) * 1
(-4 + 1x) + 8 = (x + -4)(x + 4) * 1

Reorder the terms:
-4 + 8 + 1x = (x + -4)(x + 4) * 1

Combine like terms: -4 + 8 = 4
4 + 1x = (x + -4)(x + 4) * 1

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

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

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

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

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

Solving
4 + 1x = -16 + 1x2

Solving for variable 'x'.

Reorder the terms:
4 + 16 + 1x + -1x2 = -16 + 1x2 + 16 + -1x2

Combine like terms: 4 + 16 = 20
20 + 1x + -1x2 = -16 + 1x2 + 16 + -1x2

Reorder the terms:
20 + 1x + -1x2 = -16 + 16 + 1x2 + -1x2

Combine like terms: -16 + 16 = 0
20 + 1x + -1x2 = 0 + 1x2 + -1x2
20 + 1x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
20 + 1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(4 + x) = 0

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}