(60-x)(2x-6)=180

Solution for (60-x)(2x-6)=180 equation:

Simplifying
(60 + -1x)(2x + -6) = 180

Reorder the terms:
(60 + -1x)(-6 + 2x) = 180

Multiply (60 + -1x) * (-6 + 2x)
(60(-6 + 2x) + -1x * (-6 + 2x)) = 180
((-6 * 60 + 2x * 60) + -1x * (-6 + 2x)) = 180
((-360 + 120x) + -1x * (-6 + 2x)) = 180
(-360 + 120x + (-6 * -1x + 2x * -1x)) = 180
(-360 + 120x + (6x + -2x2)) = 180

Combine like terms: 120x + 6x = 126x
(-360 + 126x + -2x2) = 180

Solving
-360 + 126x + -2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-360 + -180 + 126x + -2x2 = 180 + -180

Combine like terms: -360 + -180 = -540
-540 + 126x + -2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-540 + 126x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-270 + 63x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-270 + 63x + -1x2)' equal to zero and attempt to solve:

Simplifying
-270 + 63x + -1x2 = 0

Solving
-270 + 63x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
270 + -63x + x2 = 0

Move the constant term to the right:

Add '-270' to each side of the equation.
270 + -63x + -270 + x2 = 0 + -270

Reorder the terms:
270 + -270 + -63x + x2 = 0 + -270

Combine like terms: 270 + -270 = 0
0 + -63x + x2 = 0 + -270
-63x + x2 = 0 + -270

Combine like terms: 0 + -270 = -270
-63x + x2 = -270

The x term is -63x.  Take half its coefficient (-31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
-63x + 992.25 + x2 = -270 + 992.25

Reorder the terms:
992.25 + -63x + x2 = -270 + 992.25

Combine like terms: -270 + 992.25 = 722.25
992.25 + -63x + x2 = 722.25

Factor a perfect square on the left side:
(x + -31.5)(x + -31.5) = 722.25

Calculate the square root of the right side: 26.874709301

Break this problem into two subproblems by setting 
(x + -31.5) equal to 26.874709301 and -26.874709301.

Subproblem 1
x + -31.5 = 26.874709301

Simplifying
x + -31.5 = 26.874709301

Reorder the terms:
-31.5 + x = 26.874709301

Solving
-31.5 + x = 26.874709301

Solving for variable 'x'.

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

Add '31.5' to each side of the equation.
-31.5 + 31.5 + x = 26.874709301 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + x = 26.874709301 + 31.5
x = 26.874709301 + 31.5

Combine like terms: 26.874709301 + 31.5 = 58.374709301
x = 58.374709301

Simplifying
x = 58.374709301

Subproblem 2
x + -31.5 = -26.874709301

Simplifying
x + -31.5 = -26.874709301

Reorder the terms:
-31.5 + x = -26.874709301

Solving
-31.5 + x = -26.874709301

Solving for variable 'x'.

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

Add '31.5' to each side of the equation.
-31.5 + 31.5 + x = -26.874709301 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + x = -26.874709301 + 31.5
x = -26.874709301 + 31.5

Combine like terms: -26.874709301 + 31.5 = 4.625290699
x = 4.625290699

Simplifying
x = 4.625290699

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {58.374709301, 4.625290699}
Solution
x = {58.374709301, 4.625290699}