(8x+6)(6x+2)=148

Solution for (8x+6)(6x+2)=148 equation:

Simplifying
(8x + 6)(6x + 2) = 148

Reorder the terms:
(6 + 8x)(6x + 2) = 148

Reorder the terms:
(6 + 8x)(2 + 6x) = 148

Multiply (6 + 8x) * (2 + 6x)
(6(2 + 6x) + 8x * (2 + 6x)) = 148
((2 * 6 + 6x * 6) + 8x * (2 + 6x)) = 148
((12 + 36x) + 8x * (2 + 6x)) = 148
(12 + 36x + (2 * 8x + 6x * 8x)) = 148
(12 + 36x + (16x + 48x2)) = 148

Combine like terms: 36x + 16x = 52x
(12 + 52x + 48x2) = 148

Solving
12 + 52x + 48x2 = 148

Solving for variable 'x'.

Reorder the terms:
12 + -148 + 52x + 48x2 = 148 + -148

Combine like terms: 12 + -148 = -136
-136 + 52x + 48x2 = 148 + -148

Combine like terms: 148 + -148 = 0
-136 + 52x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-34 + 13x + 12x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-34 + 13x + 12x2)' equal to zero and attempt to solve:

Simplifying
-34 + 13x + 12x2 = 0

Solving
-34 + 13x + 12x2 = 0

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

Divide each side by '12'.
-2.833333333 + 1.083333333x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 1.083333333x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 1.083333333x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 1.083333333x + x2 = 0 + 2.833333333
1.083333333x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
1.083333333x + x2 = 2.833333333

The x term is 1.083333333x.  Take half its coefficient (0.5416666665).
Square it (0.2934027776) and add it to both sides.

Add '0.2934027776' to each side of the equation.
1.083333333x + 0.2934027776 + x2 = 2.833333333 + 0.2934027776

Reorder the terms:
0.2934027776 + 1.083333333x + x2 = 2.833333333 + 0.2934027776

Combine like terms: 2.833333333 + 0.2934027776 = 3.1267361106
0.2934027776 + 1.083333333x + x2 = 3.1267361106

Factor a perfect square on the left side:
(x + 0.5416666665)(x + 0.5416666665) = 3.1267361106

Calculate the square root of the right side: 1.768257931

Break this problem into two subproblems by setting 
(x + 0.5416666665) equal to 1.768257931 and -1.768257931.

Subproblem 1
x + 0.5416666665 = 1.768257931

Simplifying
x + 0.5416666665 = 1.768257931

Reorder the terms:
0.5416666665 + x = 1.768257931

Solving
0.5416666665 + x = 1.768257931

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = 1.768257931 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = 1.768257931 + -0.5416666665
x = 1.768257931 + -0.5416666665

Combine like terms: 1.768257931 + -0.5416666665 = 1.2265912645
x = 1.2265912645

Simplifying
x = 1.2265912645

Subproblem 2
x + 0.5416666665 = -1.768257931

Simplifying
x + 0.5416666665 = -1.768257931

Reorder the terms:
0.5416666665 + x = -1.768257931

Solving
0.5416666665 + x = -1.768257931

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = -1.768257931 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = -1.768257931 + -0.5416666665
x = -1.768257931 + -0.5416666665

Combine like terms: -1.768257931 + -0.5416666665 = -2.3099245975
x = -2.3099245975

Simplifying
x = -2.3099245975

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2265912645, -2.3099245975}
Solution
x = {1.2265912645, -2.3099245975}