(7x-3)(12x-3)=180

Solution for (7x-3)(12x-3)=180 equation:

Simplifying
(7x + -3)(12x + -3) = 180

Reorder the terms:
(-3 + 7x)(12x + -3) = 180

Reorder the terms:
(-3 + 7x)(-3 + 12x) = 180

Multiply (-3 + 7x) * (-3 + 12x)
(-3(-3 + 12x) + 7x * (-3 + 12x)) = 180
((-3 * -3 + 12x * -3) + 7x * (-3 + 12x)) = 180
((9 + -36x) + 7x * (-3 + 12x)) = 180
(9 + -36x + (-3 * 7x + 12x * 7x)) = 180
(9 + -36x + (-21x + 84x2)) = 180

Combine like terms: -36x + -21x = -57x
(9 + -57x + 84x2) = 180

Solving
9 + -57x + 84x2 = 180

Solving for variable 'x'.

Reorder the terms:
9 + -180 + -57x + 84x2 = 180 + -180

Combine like terms: 9 + -180 = -171
-171 + -57x + 84x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-171 + -57x + 84x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-57 + -19x + 28x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-57 + -19x + 28x2)' equal to zero and attempt to solve:

Simplifying
-57 + -19x + 28x2 = 0

Solving
-57 + -19x + 28x2 = 0

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

Divide each side by '28'.
-2.035714286 + -0.6785714286x + x2 = 0

Move the constant term to the right:

Add '2.035714286' to each side of the equation.
-2.035714286 + -0.6785714286x + 2.035714286 + x2 = 0 + 2.035714286

Reorder the terms:
-2.035714286 + 2.035714286 + -0.6785714286x + x2 = 0 + 2.035714286

Combine like terms: -2.035714286 + 2.035714286 = 0.000000000
0.000000000 + -0.6785714286x + x2 = 0 + 2.035714286
-0.6785714286x + x2 = 0 + 2.035714286

Combine like terms: 0 + 2.035714286 = 2.035714286
-0.6785714286x + x2 = 2.035714286

The x term is -0.6785714286x.  Take half its coefficient (-0.3392857143).
Square it (0.1151147959) and add it to both sides.

Add '0.1151147959' to each side of the equation.
-0.6785714286x + 0.1151147959 + x2 = 2.035714286 + 0.1151147959

Reorder the terms:
0.1151147959 + -0.6785714286x + x2 = 2.035714286 + 0.1151147959

Combine like terms: 2.035714286 + 0.1151147959 = 2.1508290819
0.1151147959 + -0.6785714286x + x2 = 2.1508290819

Factor a perfect square on the left side:
(x + -0.3392857143)(x + -0.3392857143) = 2.1508290819

Calculate the square root of the right side: 1.466570517

Break this problem into two subproblems by setting 
(x + -0.3392857143) equal to 1.466570517 and -1.466570517.

Subproblem 1
x + -0.3392857143 = 1.466570517

Simplifying
x + -0.3392857143 = 1.466570517

Reorder the terms:
-0.3392857143 + x = 1.466570517

Solving
-0.3392857143 + x = 1.466570517

Solving for variable 'x'.

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

Add '0.3392857143' to each side of the equation.
-0.3392857143 + 0.3392857143 + x = 1.466570517 + 0.3392857143

Combine like terms: -0.3392857143 + 0.3392857143 = 0.0000000000
0.0000000000 + x = 1.466570517 + 0.3392857143
x = 1.466570517 + 0.3392857143

Combine like terms: 1.466570517 + 0.3392857143 = 1.8058562313
x = 1.8058562313

Simplifying
x = 1.8058562313

Subproblem 2
x + -0.3392857143 = -1.466570517

Simplifying
x + -0.3392857143 = -1.466570517

Reorder the terms:
-0.3392857143 + x = -1.466570517

Solving
-0.3392857143 + x = -1.466570517

Solving for variable 'x'.

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

Add '0.3392857143' to each side of the equation.
-0.3392857143 + 0.3392857143 + x = -1.466570517 + 0.3392857143

Combine like terms: -0.3392857143 + 0.3392857143 = 0.0000000000
0.0000000000 + x = -1.466570517 + 0.3392857143
x = -1.466570517 + 0.3392857143

Combine like terms: -1.466570517 + 0.3392857143 = -1.1272848027
x = -1.1272848027

Simplifying
x = -1.1272848027

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8058562313, -1.1272848027}
Solution
x = {1.8058562313, -1.1272848027}