66=4(2x-3)2(x+4)

Solution for 66=4(2x-3)2(x+4) equation:

Simplifying
66 = 4(2x + -3) * 2(x + 4)

Reorder the terms:
66 = 4(-3 + 2x) * 2(x + 4)

Reorder the terms:
66 = 4(-3 + 2x) * 2(4 + x)

Reorder the terms for easier multiplication:
66 = 4 * 2(-3 + 2x)(4 + x)

Multiply 4 * 2
66 = 8(-3 + 2x)(4 + x)

Multiply (-3 + 2x) * (4 + x)
66 = 8(-3(4 + x) + 2x * (4 + x))
66 = 8((4 * -3 + x * -3) + 2x * (4 + x))
66 = 8((-12 + -3x) + 2x * (4 + x))
66 = 8(-12 + -3x + (4 * 2x + x * 2x))
66 = 8(-12 + -3x + (8x + 2x2))

Combine like terms: -3x + 8x = 5x
66 = 8(-12 + 5x + 2x2)
66 = (-12 * 8 + 5x * 8 + 2x2 * 8)
66 = (-96 + 40x + 16x2)

Solving
66 = -96 + 40x + 16x2

Solving for variable 'x'.

Combine like terms: 66 + 96 = 162
162 + -40x + -16x2 = -96 + 40x + 16x2 + 96 + -40x + -16x2

Reorder the terms:
162 + -40x + -16x2 = -96 + 96 + 40x + -40x + 16x2 + -16x2

Combine like terms: -96 + 96 = 0
162 + -40x + -16x2 = 0 + 40x + -40x + 16x2 + -16x2
162 + -40x + -16x2 = 40x + -40x + 16x2 + -16x2

Combine like terms: 40x + -40x = 0
162 + -40x + -16x2 = 0 + 16x2 + -16x2
162 + -40x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
162 + -40x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(81 + -20x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(81 + -20x + -8x2)' equal to zero and attempt to solve:

Simplifying
81 + -20x + -8x2 = 0

Solving
81 + -20x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-10.125 + 2.5x + x2 = 0

Move the constant term to the right:

Add '10.125' to each side of the equation.
-10.125 + 2.5x + 10.125 + x2 = 0 + 10.125

Reorder the terms:
-10.125 + 10.125 + 2.5x + x2 = 0 + 10.125

Combine like terms: -10.125 + 10.125 = 0.000
0.000 + 2.5x + x2 = 0 + 10.125
2.5x + x2 = 0 + 10.125

Combine like terms: 0 + 10.125 = 10.125
2.5x + x2 = 10.125

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 10.125 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 10.125 + 1.5625

Combine like terms: 10.125 + 1.5625 = 11.6875
1.5625 + 2.5x + x2 = 11.6875

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 11.6875

Calculate the square root of the right side: 3.418698583

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.418698583 and -3.418698583.

Subproblem 1
x + 1.25 = 3.418698583

Simplifying
x + 1.25 = 3.418698583

Reorder the terms:
1.25 + x = 3.418698583

Solving
1.25 + x = 3.418698583

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.418698583 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.418698583 + -1.25
x = 3.418698583 + -1.25

Combine like terms: 3.418698583 + -1.25 = 2.168698583
x = 2.168698583

Simplifying
x = 2.168698583

Subproblem 2
x + 1.25 = -3.418698583

Simplifying
x + 1.25 = -3.418698583

Reorder the terms:
1.25 + x = -3.418698583

Solving
1.25 + x = -3.418698583

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.418698583 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.418698583 + -1.25
x = -3.418698583 + -1.25

Combine like terms: -3.418698583 + -1.25 = -4.668698583
x = -4.668698583

Simplifying
x = -4.668698583

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.168698583, -4.668698583}
Solution
x = {2.168698583, -4.668698583}