2x(x+66)=180

Solution for 2x(x+66)=180 equation:

Simplifying
2x(x + 66) = 180

Reorder the terms:
2x(66 + x) = 180
(66 * 2x + x * 2x) = 180
(132x + 2x2) = 180

Solving
132x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 132x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 132x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 66x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-90 + 66x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 66x + x2 = 0

Solving
-90 + 66x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 66x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 66x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 66x + x2 = 0 + 90
66x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
66x + x2 = 90

The x term is 66x.  Take half its coefficient (33).
Square it (1089) and add it to both sides.

Add '1089' to each side of the equation.
66x + 1089 + x2 = 90 + 1089

Reorder the terms:
1089 + 66x + x2 = 90 + 1089

Combine like terms: 90 + 1089 = 1179
1089 + 66x + x2 = 1179

Factor a perfect square on the left side:
(x + 33)(x + 33) = 1179

Calculate the square root of the right side: 34.336569427

Break this problem into two subproblems by setting 
(x + 33) equal to 34.336569427 and -34.336569427.

Subproblem 1
x + 33 = 34.336569427

Simplifying
x + 33 = 34.336569427

Reorder the terms:
33 + x = 34.336569427

Solving
33 + x = 34.336569427

Solving for variable 'x'.

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

Add '-33' to each side of the equation.
33 + -33 + x = 34.336569427 + -33

Combine like terms: 33 + -33 = 0
0 + x = 34.336569427 + -33
x = 34.336569427 + -33

Combine like terms: 34.336569427 + -33 = 1.336569427
x = 1.336569427

Simplifying
x = 1.336569427

Subproblem 2
x + 33 = -34.336569427

Simplifying
x + 33 = -34.336569427

Reorder the terms:
33 + x = -34.336569427

Solving
33 + x = -34.336569427

Solving for variable 'x'.

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

Add '-33' to each side of the equation.
33 + -33 + x = -34.336569427 + -33

Combine like terms: 33 + -33 = 0
0 + x = -34.336569427 + -33
x = -34.336569427 + -33

Combine like terms: -34.336569427 + -33 = -67.336569427
x = -67.336569427

Simplifying
x = -67.336569427

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.336569427, -67.336569427}
Solution
x = {1.336569427, -67.336569427}