(7x-1)(3x-9)=180

Solution for (7x-1)(3x-9)=180 equation:

Simplifying
(7x + -1)(3x + -9) = 180

Reorder the terms:
(-1 + 7x)(3x + -9) = 180

Reorder the terms:
(-1 + 7x)(-9 + 3x) = 180

Multiply (-1 + 7x) * (-9 + 3x)
(-1(-9 + 3x) + 7x * (-9 + 3x)) = 180
((-9 * -1 + 3x * -1) + 7x * (-9 + 3x)) = 180
((9 + -3x) + 7x * (-9 + 3x)) = 180
(9 + -3x + (-9 * 7x + 3x * 7x)) = 180
(9 + -3x + (-63x + 21x2)) = 180

Combine like terms: -3x + -63x = -66x
(9 + -66x + 21x2) = 180

Solving
9 + -66x + 21x2 = 180

Solving for variable 'x'.

Reorder the terms:
9 + -180 + -66x + 21x2 = 180 + -180

Combine like terms: 9 + -180 = -171
-171 + -66x + 21x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-171 + -66x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-57 + -22x + 7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-57 + -22x + 7x2)' equal to zero and attempt to solve:

Simplifying
-57 + -22x + 7x2 = 0

Solving
-57 + -22x + 7x2 = 0

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

Divide each side by '7'.
-8.142857143 + -3.142857143x + x2 = 0

Move the constant term to the right:

Add '8.142857143' to each side of the equation.
-8.142857143 + -3.142857143x + 8.142857143 + x2 = 0 + 8.142857143

Reorder the terms:
-8.142857143 + 8.142857143 + -3.142857143x + x2 = 0 + 8.142857143

Combine like terms: -8.142857143 + 8.142857143 = 0.000000000
0.000000000 + -3.142857143x + x2 = 0 + 8.142857143
-3.142857143x + x2 = 0 + 8.142857143

Combine like terms: 0 + 8.142857143 = 8.142857143
-3.142857143x + x2 = 8.142857143

The x term is -3.142857143x.  Take half its coefficient (-1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
-3.142857143x + 2.469387757 + x2 = 8.142857143 + 2.469387757

Reorder the terms:
2.469387757 + -3.142857143x + x2 = 8.142857143 + 2.469387757

Combine like terms: 8.142857143 + 2.469387757 = 10.6122449
2.469387757 + -3.142857143x + x2 = 10.6122449

Factor a perfect square on the left side:
(x + -1.571428572)(x + -1.571428572) = 10.6122449

Calculate the square root of the right side: 3.257644072

Break this problem into two subproblems by setting 
(x + -1.571428572) equal to 3.257644072 and -3.257644072.

Subproblem 1
x + -1.571428572 = 3.257644072

Simplifying
x + -1.571428572 = 3.257644072

Reorder the terms:
-1.571428572 + x = 3.257644072

Solving
-1.571428572 + x = 3.257644072

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = 3.257644072 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = 3.257644072 + 1.571428572
x = 3.257644072 + 1.571428572

Combine like terms: 3.257644072 + 1.571428572 = 4.829072644
x = 4.829072644

Simplifying
x = 4.829072644

Subproblem 2
x + -1.571428572 = -3.257644072

Simplifying
x + -1.571428572 = -3.257644072

Reorder the terms:
-1.571428572 + x = -3.257644072

Solving
-1.571428572 + x = -3.257644072

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = -3.257644072 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = -3.257644072 + 1.571428572
x = -3.257644072 + 1.571428572

Combine like terms: -3.257644072 + 1.571428572 = -1.6862155
x = -1.6862155

Simplifying
x = -1.6862155

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.829072644, -1.6862155}
Solution
x = {4.829072644, -1.6862155}