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

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

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

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

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

Multiply (-3 + 7x) * (-7 + 12x)
180 = (-3(-7 + 12x) + 7x * (-7 + 12x))
180 = ((-7 * -3 + 12x * -3) + 7x * (-7 + 12x))
180 = ((21 + -36x) + 7x * (-7 + 12x))
180 = (21 + -36x + (-7 * 7x + 12x * 7x))
180 = (21 + -36x + (-49x + 84x2))

Combine like terms: -36x + -49x = -85x
180 = (21 + -85x + 84x2)

Solving
180 = 21 + -85x + 84x2

Solving for variable 'x'.

Combine like terms: 180 + -21 = 159
159 + 85x + -84x2 = 21 + -85x + 84x2 + -21 + 85x + -84x2

Reorder the terms:
159 + 85x + -84x2 = 21 + -21 + -85x + 85x + 84x2 + -84x2

Combine like terms: 21 + -21 = 0
159 + 85x + -84x2 = 0 + -85x + 85x + 84x2 + -84x2
159 + 85x + -84x2 = -85x + 85x + 84x2 + -84x2

Combine like terms: -85x + 85x = 0
159 + 85x + -84x2 = 0 + 84x2 + -84x2
159 + 85x + -84x2 = 84x2 + -84x2

Combine like terms: 84x2 + -84x2 = 0
159 + 85x + -84x2 = 0

Begin completing the square.  Divide all terms by
-84 the coefficient of the squared term: 

Divide each side by '-84'.
-1.892857143 + -1.011904762x + x2 = 0

Move the constant term to the right:

Add '1.892857143' to each side of the equation.
-1.892857143 + -1.011904762x + 1.892857143 + x2 = 0 + 1.892857143

Reorder the terms:
-1.892857143 + 1.892857143 + -1.011904762x + x2 = 0 + 1.892857143

Combine like terms: -1.892857143 + 1.892857143 = 0.000000000
0.000000000 + -1.011904762x + x2 = 0 + 1.892857143
-1.011904762x + x2 = 0 + 1.892857143

Combine like terms: 0 + 1.892857143 = 1.892857143
-1.011904762x + x2 = 1.892857143

The x term is -1.011904762x.  Take half its coefficient (-0.505952381).
Square it (0.2559878118) and add it to both sides.

Add '0.2559878118' to each side of the equation.
-1.011904762x + 0.2559878118 + x2 = 1.892857143 + 0.2559878118

Reorder the terms:
0.2559878118 + -1.011904762x + x2 = 1.892857143 + 0.2559878118

Combine like terms: 1.892857143 + 0.2559878118 = 2.1488449548
0.2559878118 + -1.011904762x + x2 = 2.1488449548

Factor a perfect square on the left side:
(x + -0.505952381)(x + -0.505952381) = 2.1488449548

Calculate the square root of the right side: 1.46589391

Break this problem into two subproblems by setting 
(x + -0.505952381) equal to 1.46589391 and -1.46589391.

Subproblem 1
x + -0.505952381 = 1.46589391

Simplifying
x + -0.505952381 = 1.46589391

Reorder the terms:
-0.505952381 + x = 1.46589391

Solving
-0.505952381 + x = 1.46589391

Solving for variable 'x'.

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

Add '0.505952381' to each side of the equation.
-0.505952381 + 0.505952381 + x = 1.46589391 + 0.505952381

Combine like terms: -0.505952381 + 0.505952381 = 0.000000000
0.000000000 + x = 1.46589391 + 0.505952381
x = 1.46589391 + 0.505952381

Combine like terms: 1.46589391 + 0.505952381 = 1.971846291
x = 1.971846291

Simplifying
x = 1.971846291

Subproblem 2
x + -0.505952381 = -1.46589391

Simplifying
x + -0.505952381 = -1.46589391

Reorder the terms:
-0.505952381 + x = -1.46589391

Solving
-0.505952381 + x = -1.46589391

Solving for variable 'x'.

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

Add '0.505952381' to each side of the equation.
-0.505952381 + 0.505952381 + x = -1.46589391 + 0.505952381

Combine like terms: -0.505952381 + 0.505952381 = 0.000000000
0.000000000 + x = -1.46589391 + 0.505952381
x = -1.46589391 + 0.505952381

Combine like terms: -1.46589391 + 0.505952381 = -0.959941529
x = -0.959941529

Simplifying
x = -0.959941529

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.971846291, -0.959941529}