(x+5)(x+5)=100

Solution for (x+5)(x+5)=100 equation:

Simplifying
(x + 5)(x + 5) = 100

Reorder the terms:
(5 + x)(x + 5) = 100

Reorder the terms:
(5 + x)(5 + x) = 100

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) = 100
((5 * 5 + x * 5) + x(5 + x)) = 100
((25 + 5x) + x(5 + x)) = 100
(25 + 5x + (5 * x + x * x)) = 100
(25 + 5x + (5x + x2)) = 100

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) = 100

Solving
25 + 10x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
25 + -100 + 10x + x2 = 100 + -100

Combine like terms: 25 + -100 = -75
-75 + 10x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-75 + 10x + x2 = 0

Factor a trinomial.
(-15 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

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

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

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
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
Solution
x = {-15, 5}