(2x+4)(2x+4)=64

Solution for (2x+4)(2x+4)=64 equation:

Simplifying
(2x + 4)(2x + 4) = 64

Reorder the terms:
(4 + 2x)(2x + 4) = 64

Reorder the terms:
(4 + 2x)(4 + 2x) = 64

Multiply (4 + 2x) * (4 + 2x)
(4(4 + 2x) + 2x * (4 + 2x)) = 64
((4 * 4 + 2x * 4) + 2x * (4 + 2x)) = 64
((16 + 8x) + 2x * (4 + 2x)) = 64
(16 + 8x + (4 * 2x + 2x * 2x)) = 64
(16 + 8x + (8x + 4x2)) = 64

Combine like terms: 8x + 8x = 16x
(16 + 16x + 4x2) = 64

Solving
16 + 16x + 4x2 = 64

Solving for variable 'x'.

Reorder the terms:
16 + -64 + 16x + 4x2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + 16x + 4x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 4x + x2) = 0

Factor a trinomial.
4((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
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
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 = {-6, 2}