80x(3x-22)=180

Solution for 80x(3x-22)=180 equation:

Simplifying
80x(3x + -22) = 180

Reorder the terms:
80x(-22 + 3x) = 180
(-22 * 80x + 3x * 80x) = 180
(-1760x + 240x2) = 180

Solving
-1760x + 240x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -1760x + 240x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -1760x + 240x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-9 + -88x + 12x2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-9 + -88x + 12x2)' equal to zero and attempt to solve:

Simplifying
-9 + -88x + 12x2 = 0

Solving
-9 + -88x + 12x2 = 0

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

Divide each side by '12'.
-0.75 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -7.333333333x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -7.333333333x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -7.333333333x + x2 = 0 + 0.75
-7.333333333x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-7.333333333x + x2 = 0.75

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 0.75 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 0.75 + 13.44444445

Combine like terms: 0.75 + 13.44444445 = 14.19444445
13.44444445 + -7.333333333x + x2 = 14.19444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 14.19444445

Calculate the square root of the right side: 3.767551519

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 3.767551519 and -3.767551519.

Subproblem 1
x + -3.666666667 = 3.767551519

Simplifying
x + -3.666666667 = 3.767551519

Reorder the terms:
-3.666666667 + x = 3.767551519

Solving
-3.666666667 + x = 3.767551519

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 3.767551519 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 3.767551519 + 3.666666667
x = 3.767551519 + 3.666666667

Combine like terms: 3.767551519 + 3.666666667 = 7.434218186
x = 7.434218186

Simplifying
x = 7.434218186

Subproblem 2
x + -3.666666667 = -3.767551519

Simplifying
x + -3.666666667 = -3.767551519

Reorder the terms:
-3.666666667 + x = -3.767551519

Solving
-3.666666667 + x = -3.767551519

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -3.767551519 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -3.767551519 + 3.666666667
x = -3.767551519 + 3.666666667

Combine like terms: -3.767551519 + 3.666666667 = -0.100884852
x = -0.100884852

Simplifying
x = -0.100884852

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.434218186, -0.100884852}
Solution
x = {7.434218186, -0.100884852}