(8x+12)(5x+57)=180

Solution for (8x+12)(5x+57)=180 equation:

Simplifying
(8x + 12)(5x + 57) = 180

Reorder the terms:
(12 + 8x)(5x + 57) = 180

Reorder the terms:
(12 + 8x)(57 + 5x) = 180

Multiply (12 + 8x) * (57 + 5x)
(12(57 + 5x) + 8x * (57 + 5x)) = 180
((57 * 12 + 5x * 12) + 8x * (57 + 5x)) = 180
((684 + 60x) + 8x * (57 + 5x)) = 180
(684 + 60x + (57 * 8x + 5x * 8x)) = 180
(684 + 60x + (456x + 40x2)) = 180

Combine like terms: 60x + 456x = 516x
(684 + 516x + 40x2) = 180

Solving
684 + 516x + 40x2 = 180

Solving for variable 'x'.

Reorder the terms:
684 + -180 + 516x + 40x2 = 180 + -180

Combine like terms: 684 + -180 = 504
504 + 516x + 40x2 = 180 + -180

Combine like terms: 180 + -180 = 0
504 + 516x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(126 + 129x + 10x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(126 + 129x + 10x2)' equal to zero and attempt to solve:

Simplifying
126 + 129x + 10x2 = 0

Solving
126 + 129x + 10x2 = 0

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

Divide each side by '10'.
12.6 + 12.9x + x2 = 0.0

Move the constant term to the right:

Add '-12.6' to each side of the equation.
12.6 + 12.9x + -12.6 + x2 = 0.0 + -12.6

Reorder the terms:
12.6 + -12.6 + 12.9x + x2 = 0.0 + -12.6

Combine like terms: 12.6 + -12.6 = 0.0
0.0 + 12.9x + x2 = 0.0 + -12.6
12.9x + x2 = 0.0 + -12.6

Combine like terms: 0.0 + -12.6 = -12.6
12.9x + x2 = -12.6

The x term is 12.9x.  Take half its coefficient (6.45).
Square it (41.6025) and add it to both sides.

Add '41.6025' to each side of the equation.
12.9x + 41.6025 + x2 = -12.6 + 41.6025

Reorder the terms:
41.6025 + 12.9x + x2 = -12.6 + 41.6025

Combine like terms: -12.6 + 41.6025 = 29.0025
41.6025 + 12.9x + x2 = 29.0025

Factor a perfect square on the left side:
(x + 6.45)(x + 6.45) = 29.0025

Calculate the square root of the right side: 5.385396921

Break this problem into two subproblems by setting 
(x + 6.45) equal to 5.385396921 and -5.385396921.

Subproblem 1
x + 6.45 = 5.385396921

Simplifying
x + 6.45 = 5.385396921

Reorder the terms:
6.45 + x = 5.385396921

Solving
6.45 + x = 5.385396921

Solving for variable 'x'.

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

Add '-6.45' to each side of the equation.
6.45 + -6.45 + x = 5.385396921 + -6.45

Combine like terms: 6.45 + -6.45 = 0.00
0.00 + x = 5.385396921 + -6.45
x = 5.385396921 + -6.45

Combine like terms: 5.385396921 + -6.45 = -1.064603079
x = -1.064603079

Simplifying
x = -1.064603079

Subproblem 2
x + 6.45 = -5.385396921

Simplifying
x + 6.45 = -5.385396921

Reorder the terms:
6.45 + x = -5.385396921

Solving
6.45 + x = -5.385396921

Solving for variable 'x'.

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

Add '-6.45' to each side of the equation.
6.45 + -6.45 + x = -5.385396921 + -6.45

Combine like terms: 6.45 + -6.45 = 0.00
0.00 + x = -5.385396921 + -6.45
x = -5.385396921 + -6.45

Combine like terms: -5.385396921 + -6.45 = -11.835396921
x = -11.835396921

Simplifying
x = -11.835396921

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.064603079, -11.835396921}
Solution
x = {-1.064603079, -11.835396921}