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

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

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

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

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

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

Combine like terms: 25x + 25x = 50x
(25 + 50x + 25x2) = 100

Solving
25 + 50x + 25x2 = 100

Solving for variable 'x'.

Reorder the terms:
25 + -100 + 50x + 25x2 = 100 + -100

Combine like terms: 25 + -100 = -75
-75 + 50x + 25x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-75 + 50x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-3 + 2x + x2) = 0

Factor a trinomial.
25((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-3, 1}