(6x+2)(3x+4)=64

Solution for (6x+2)(3x+4)=64 equation:

Simplifying
(6x + 2)(3x + 4) = 64

Reorder the terms:
(2 + 6x)(3x + 4) = 64

Reorder the terms:
(2 + 6x)(4 + 3x) = 64

Multiply (2 + 6x) * (4 + 3x)
(2(4 + 3x) + 6x * (4 + 3x)) = 64
((4 * 2 + 3x * 2) + 6x * (4 + 3x)) = 64
((8 + 6x) + 6x * (4 + 3x)) = 64
(8 + 6x + (4 * 6x + 3x * 6x)) = 64
(8 + 6x + (24x + 18x2)) = 64

Combine like terms: 6x + 24x = 30x
(8 + 30x + 18x2) = 64

Solving
8 + 30x + 18x2 = 64

Solving for variable 'x'.

Reorder the terms:
8 + -64 + 30x + 18x2 = 64 + -64

Combine like terms: 8 + -64 = -56
-56 + 30x + 18x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-56 + 30x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 15x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-28 + 15x + 9x2)' equal to zero and attempt to solve:

Simplifying
-28 + 15x + 9x2 = 0

Solving
-28 + 15x + 9x2 = 0

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

Divide each side by '9'.
-3.111111111 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + 1.666666667x + 3.111111111 + x2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + 1.666666667x + x2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 3.111111111
1.666666667x + x2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
1.666666667x + x2 = 3.111111111

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 3.111111111 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 3.111111111 + 0.6944444447

Combine like terms: 3.111111111 + 0.6944444447 = 3.8055555557
0.6944444447 + 1.666666667x + x2 = 3.8055555557

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 3.8055555557

Calculate the square root of the right side: 1.950783318

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.950783318 and -1.950783318.

Subproblem 1
x + 0.8333333335 = 1.950783318

Simplifying
x + 0.8333333335 = 1.950783318

Reorder the terms:
0.8333333335 + x = 1.950783318

Solving
0.8333333335 + x = 1.950783318

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.950783318 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.950783318 + -0.8333333335
x = 1.950783318 + -0.8333333335

Combine like terms: 1.950783318 + -0.8333333335 = 1.1174499845
x = 1.1174499845

Simplifying
x = 1.1174499845

Subproblem 2
x + 0.8333333335 = -1.950783318

Simplifying
x + 0.8333333335 = -1.950783318

Reorder the terms:
0.8333333335 + x = -1.950783318

Solving
0.8333333335 + x = -1.950783318

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.950783318 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.950783318 + -0.8333333335
x = -1.950783318 + -0.8333333335

Combine like terms: -1.950783318 + -0.8333333335 = -2.7841166515
x = -2.7841166515

Simplifying
x = -2.7841166515

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1174499845, -2.7841166515}
Solution
x = {1.1174499845, -2.7841166515}