(5x-33)(6x+4)=180

Solution for (5x-33)(6x+4)=180 equation:

Simplifying
(5x + -33)(6x + 4) = 180

Reorder the terms:
(-33 + 5x)(6x + 4) = 180

Reorder the terms:
(-33 + 5x)(4 + 6x) = 180

Multiply (-33 + 5x) * (4 + 6x)
(-33(4 + 6x) + 5x * (4 + 6x)) = 180
((4 * -33 + 6x * -33) + 5x * (4 + 6x)) = 180
((-132 + -198x) + 5x * (4 + 6x)) = 180
(-132 + -198x + (4 * 5x + 6x * 5x)) = 180
(-132 + -198x + (20x + 30x2)) = 180

Combine like terms: -198x + 20x = -178x
(-132 + -178x + 30x2) = 180

Solving
-132 + -178x + 30x2 = 180

Solving for variable 'x'.

Reorder the terms:
-132 + -180 + -178x + 30x2 = 180 + -180

Combine like terms: -132 + -180 = -312
-312 + -178x + 30x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-312 + -178x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-156 + -89x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-156 + -89x + 15x2)' equal to zero and attempt to solve:

Simplifying
-156 + -89x + 15x2 = 0

Solving
-156 + -89x + 15x2 = 0

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

Divide each side by '15'.
-10.4 + -5.933333333x + x2 = 0

Move the constant term to the right:

Add '10.4' to each side of the equation.
-10.4 + -5.933333333x + 10.4 + x2 = 0 + 10.4

Reorder the terms:
-10.4 + 10.4 + -5.933333333x + x2 = 0 + 10.4

Combine like terms: -10.4 + 10.4 = 0.0
0.0 + -5.933333333x + x2 = 0 + 10.4
-5.933333333x + x2 = 0 + 10.4

Combine like terms: 0 + 10.4 = 10.4
-5.933333333x + x2 = 10.4

The x term is -5.933333333x.  Take half its coefficient (-2.966666667).
Square it (8.801111113) and add it to both sides.

Add '8.801111113' to each side of the equation.
-5.933333333x + 8.801111113 + x2 = 10.4 + 8.801111113

Reorder the terms:
8.801111113 + -5.933333333x + x2 = 10.4 + 8.801111113

Combine like terms: 10.4 + 8.801111113 = 19.201111113
8.801111113 + -5.933333333x + x2 = 19.201111113

Factor a perfect square on the left side:
(x + -2.966666667)(x + -2.966666667) = 19.201111113

Calculate the square root of the right side: 4.381907246

Break this problem into two subproblems by setting 
(x + -2.966666667) equal to 4.381907246 and -4.381907246.

Subproblem 1
x + -2.966666667 = 4.381907246

Simplifying
x + -2.966666667 = 4.381907246

Reorder the terms:
-2.966666667 + x = 4.381907246

Solving
-2.966666667 + x = 4.381907246

Solving for variable 'x'.

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

Add '2.966666667' to each side of the equation.
-2.966666667 + 2.966666667 + x = 4.381907246 + 2.966666667

Combine like terms: -2.966666667 + 2.966666667 = 0.000000000
0.000000000 + x = 4.381907246 + 2.966666667
x = 4.381907246 + 2.966666667

Combine like terms: 4.381907246 + 2.966666667 = 7.348573913
x = 7.348573913

Simplifying
x = 7.348573913

Subproblem 2
x + -2.966666667 = -4.381907246

Simplifying
x + -2.966666667 = -4.381907246

Reorder the terms:
-2.966666667 + x = -4.381907246

Solving
-2.966666667 + x = -4.381907246

Solving for variable 'x'.

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

Add '2.966666667' to each side of the equation.
-2.966666667 + 2.966666667 + x = -4.381907246 + 2.966666667

Combine like terms: -2.966666667 + 2.966666667 = 0.000000000
0.000000000 + x = -4.381907246 + 2.966666667
x = -4.381907246 + 2.966666667

Combine like terms: -4.381907246 + 2.966666667 = -1.415240579
x = -1.415240579

Simplifying
x = -1.415240579

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.348573913, -1.415240579}
Solution
x = {7.348573913, -1.415240579}