(x+5)(x+5)=1

Solution for (x+5)(x+5)=1 equation:

Simplifying
(x + 5)(x + 5) = 1

Reorder the terms:
(5 + x)(x + 5) = 1

Reorder the terms:
(5 + x)(5 + x) = 1

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) = 1
((5 * 5 + x * 5) + x(5 + x)) = 1
((25 + 5x) + x(5 + x)) = 1
(25 + 5x + (5 * x + x * x)) = 1
(25 + 5x + (5x + x2)) = 1

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) = 1

Solving
25 + 10x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
25 + -1 + 10x + x2 = 1 + -1

Combine like terms: 25 + -1 = 24
24 + 10x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
24 + 10x + x2 = 0

Factor a trinomial.
(6 + x)(4 + x) = 0

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
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 = {-6, -4}