x^2+(x+2)(x+2)=100

Solution for x^2+(x+2)(x+2)=100 equation:

Simplifying
x2 + (x + 2)(x + 2) = 100

Reorder the terms:
x2 + (2 + x)(x + 2) = 100

Reorder the terms:
x2 + (2 + x)(2 + x) = 100

Multiply (2 + x) * (2 + x)
x2 + (2(2 + x) + x(2 + x)) = 100
x2 + ((2 * 2 + x * 2) + x(2 + x)) = 100
x2 + ((4 + 2x) + x(2 + x)) = 100
x2 + (4 + 2x + (2 * x + x * x)) = 100
x2 + (4 + 2x + (2x + x2)) = 100

Combine like terms: 2x + 2x = 4x
x2 + (4 + 4x + x2) = 100

Reorder the terms:
4 + 4x + x2 + x2 = 100

Combine like terms: x2 + x2 = 2x2
4 + 4x + 2x2 = 100

Solving
4 + 4x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
4 + -100 + 4x + 2x2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + 4x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 2x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-8, 6}