2(x+1)(x+1)-18=0

Solution for 2(x+1)(x+1)-18=0 equation:

Simplifying
2(x + 1)(x + 1) + -18 = 0

Reorder the terms:
2(1 + x)(x + 1) + -18 = 0

Reorder the terms:
2(1 + x)(1 + x) + -18 = 0

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) + -18 = 0
2((1 * 1 + x * 1) + x(1 + x)) + -18 = 0
2((1 + 1x) + x(1 + x)) + -18 = 0
2(1 + 1x + (1 * x + x * x)) + -18 = 0
2(1 + 1x + (1x + x2)) + -18 = 0

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) + -18 = 0
(1 * 2 + 2x * 2 + x2 * 2) + -18 = 0
(2 + 4x + 2x2) + -18 = 0

Reorder the terms:
2 + -18 + 4x + 2x2 = 0

Combine like terms: 2 + -18 = -16
-16 + 4x + 2x2 = 0

Solving
-16 + 4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 2x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}