(57-5x)(18x+6)=180

Solution for (57-5x)(18x+6)=180 equation:

Simplifying
(57 + -5x)(18x + 6) = 180

Reorder the terms:
(57 + -5x)(6 + 18x) = 180

Multiply (57 + -5x) * (6 + 18x)
(57(6 + 18x) + -5x * (6 + 18x)) = 180
((6 * 57 + 18x * 57) + -5x * (6 + 18x)) = 180
((342 + 1026x) + -5x * (6 + 18x)) = 180
(342 + 1026x + (6 * -5x + 18x * -5x)) = 180
(342 + 1026x + (-30x + -90x2)) = 180

Combine like terms: 1026x + -30x = 996x
(342 + 996x + -90x2) = 180

Solving
342 + 996x + -90x2 = 180

Solving for variable 'x'.

Reorder the terms:
342 + -180 + 996x + -90x2 = 180 + -180

Combine like terms: 342 + -180 = 162
162 + 996x + -90x2 = 180 + -180

Combine like terms: 180 + -180 = 0
162 + 996x + -90x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(27 + 166x + -15x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(27 + 166x + -15x2)' equal to zero and attempt to solve:

Simplifying
27 + 166x + -15x2 = 0

Solving
27 + 166x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1.8 + -11.06666667x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -11.06666667x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -11.06666667x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -11.06666667x + x2 = 0 + 1.8
-11.06666667x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-11.06666667x + x2 = 1.8

The x term is -11.06666667x.  Take half its coefficient (-5.533333335).
Square it (30.61777780) and add it to both sides.

Add '30.61777780' to each side of the equation.
-11.06666667x + 30.61777780 + x2 = 1.8 + 30.61777780

Reorder the terms:
30.61777780 + -11.06666667x + x2 = 1.8 + 30.61777780

Combine like terms: 1.8 + 30.61777780 = 32.4177778
30.61777780 + -11.06666667x + x2 = 32.4177778

Factor a perfect square on the left side:
(x + -5.533333335)(x + -5.533333335) = 32.4177778

Calculate the square root of the right side: 5.693661195

Break this problem into two subproblems by setting 
(x + -5.533333335) equal to 5.693661195 and -5.693661195.

Subproblem 1
x + -5.533333335 = 5.693661195

Simplifying
x + -5.533333335 = 5.693661195

Reorder the terms:
-5.533333335 + x = 5.693661195

Solving
-5.533333335 + x = 5.693661195

Solving for variable 'x'.

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

Add '5.533333335' to each side of the equation.
-5.533333335 + 5.533333335 + x = 5.693661195 + 5.533333335

Combine like terms: -5.533333335 + 5.533333335 = 0.000000000
0.000000000 + x = 5.693661195 + 5.533333335
x = 5.693661195 + 5.533333335

Combine like terms: 5.693661195 + 5.533333335 = 11.22699453
x = 11.22699453

Simplifying
x = 11.22699453

Subproblem 2
x + -5.533333335 = -5.693661195

Simplifying
x + -5.533333335 = -5.693661195

Reorder the terms:
-5.533333335 + x = -5.693661195

Solving
-5.533333335 + x = -5.693661195

Solving for variable 'x'.

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

Add '5.533333335' to each side of the equation.
-5.533333335 + 5.533333335 + x = -5.693661195 + 5.533333335

Combine like terms: -5.533333335 + 5.533333335 = 0.000000000
0.000000000 + x = -5.693661195 + 5.533333335
x = -5.693661195 + 5.533333335

Combine like terms: -5.693661195 + 5.533333335 = -0.16032786
x = -0.16032786

Simplifying
x = -0.16032786

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.22699453, -0.16032786}
Solution
x = {11.22699453, -0.16032786}