[x+4][x+4]=1

Solution for [x+4][x+4]=1 equation:

Simplifying
[x + 4][x + 4] = 1

Reorder the terms:
[4 + x][x + 4] = 1

Reorder the terms:
[4 + x][4 + x] = 1

Multiply [4 + x] * [4 + x]
[4[4 + x] + x[4 + x]] = 1
[[4 * 4 + x * 4] + x[4 + x]] = 1
[[16 + 4x] + x[4 + x]] = 1
[16 + 4x + [4 * x + x * x]] = 1
[16 + 4x + [4x + x2]] = 1

Combine like terms: 4x + 4x = 8x
[16 + 8x + x2] = 1

Solving
16 + 8x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
16 + -1 + 8x + x2 = 1 + -1

Combine like terms: 16 + -1 = 15
15 + 8x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
15 + 8x + x2 = 0

Factor a trinomial.
(5 + x)(3 + x) = 0

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

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {-5, -3}