(4x+2)(4x+2)-36=0

Solution for (4x+2)(4x+2)-36=0 equation:

Simplifying
(4x + 2)(4x + 2) + -36 = 0

Reorder the terms:
(2 + 4x)(4x + 2) + -36 = 0

Reorder the terms:
(2 + 4x)(2 + 4x) + -36 = 0

Multiply (2 + 4x) * (2 + 4x)
(2(2 + 4x) + 4x * (2 + 4x)) + -36 = 0
((2 * 2 + 4x * 2) + 4x * (2 + 4x)) + -36 = 0
((4 + 8x) + 4x * (2 + 4x)) + -36 = 0
(4 + 8x + (2 * 4x + 4x * 4x)) + -36 = 0
(4 + 8x + (8x + 16x2)) + -36 = 0

Combine like terms: 8x + 8x = 16x
(4 + 16x + 16x2) + -36 = 0

Reorder the terms:
4 + -36 + 16x + 16x2 = 0

Combine like terms: 4 + -36 = -32
-32 + 16x + 16x2 = 0

Solving
-32 + 16x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + x + x2) = 0

Factor a trinomial.
16((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
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
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 = {-2, 1}