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

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

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

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

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

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

Combine like terms: 2x + 2x = 4x
4(4 + 4x + x2) = 64
(4 * 4 + 4x * 4 + x2 * 4) = 64
(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}