(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}