(12x+2)(7x+7)=180

Solution for (12x+2)(7x+7)=180 equation:

Simplifying
(12x + 2)(7x + 7) = 180

Reorder the terms:
(2 + 12x)(7x + 7) = 180

Reorder the terms:
(2 + 12x)(7 + 7x) = 180

Multiply (2 + 12x) * (7 + 7x)
(2(7 + 7x) + 12x * (7 + 7x)) = 180
((7 * 2 + 7x * 2) + 12x * (7 + 7x)) = 180
((14 + 14x) + 12x * (7 + 7x)) = 180
(14 + 14x + (7 * 12x + 7x * 12x)) = 180
(14 + 14x + (84x + 84x2)) = 180

Combine like terms: 14x + 84x = 98x
(14 + 98x + 84x2) = 180

Solving
14 + 98x + 84x2 = 180

Solving for variable 'x'.

Reorder the terms:
14 + -180 + 98x + 84x2 = 180 + -180

Combine like terms: 14 + -180 = -166
-166 + 98x + 84x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-166 + 98x + 84x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-83 + 49x + 42x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-83 + 49x + 42x2)' equal to zero and attempt to solve:

Simplifying
-83 + 49x + 42x2 = 0

Solving
-83 + 49x + 42x2 = 0

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

Divide each side by '42'.
-1.976190476 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '1.976190476' to each side of the equation.
-1.976190476 + 1.166666667x + 1.976190476 + x2 = 0 + 1.976190476

Reorder the terms:
-1.976190476 + 1.976190476 + 1.166666667x + x2 = 0 + 1.976190476

Combine like terms: -1.976190476 + 1.976190476 = 0.000000000
0.000000000 + 1.166666667x + x2 = 0 + 1.976190476
1.166666667x + x2 = 0 + 1.976190476

Combine like terms: 0 + 1.976190476 = 1.976190476
1.166666667x + x2 = 1.976190476

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = 1.976190476 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = 1.976190476 + 0.3402777780

Combine like terms: 1.976190476 + 0.3402777780 = 2.316468254
0.3402777780 + 1.166666667x + x2 = 2.316468254

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 2.316468254

Calculate the square root of the right side: 1.521994827

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 1.521994827 and -1.521994827.

Subproblem 1
x + 0.5833333335 = 1.521994827

Simplifying
x + 0.5833333335 = 1.521994827

Reorder the terms:
0.5833333335 + x = 1.521994827

Solving
0.5833333335 + x = 1.521994827

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = 1.521994827 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = 1.521994827 + -0.5833333335
x = 1.521994827 + -0.5833333335

Combine like terms: 1.521994827 + -0.5833333335 = 0.9386614935
x = 0.9386614935

Simplifying
x = 0.9386614935

Subproblem 2
x + 0.5833333335 = -1.521994827

Simplifying
x + 0.5833333335 = -1.521994827

Reorder the terms:
0.5833333335 + x = -1.521994827

Solving
0.5833333335 + x = -1.521994827

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = -1.521994827 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = -1.521994827 + -0.5833333335
x = -1.521994827 + -0.5833333335

Combine like terms: -1.521994827 + -0.5833333335 = -2.1053281605
x = -2.1053281605

Simplifying
x = -2.1053281605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9386614935, -2.1053281605}
Solution
x = {0.9386614935, -2.1053281605}