180=3x(x+8)

Solution for 180=3x(x+8) equation:

Simplifying
180 = 3x(x + 8)

Reorder the terms:
180 = 3x(8 + x)
180 = (8 * 3x + x * 3x)
180 = (24x + 3x2)

Solving
180 = 24x + 3x2

Solving for variable 'x'.

Reorder the terms:
180 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2

Combine like terms: 24x + -24x = 0
180 + -24x + -3x2 = 0 + 3x2 + -3x2
180 + -24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
180 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(60 + -8x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(60 + -8x + -1x2)' equal to zero and attempt to solve:

Simplifying
60 + -8x + -1x2 = 0

Solving
60 + -8x + -1x2 = 0

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

Divide each side by '-1'.
-60 + 8x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 8x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 8x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 8x + x2 = 0 + 60
8x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
8x + x2 = 60

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 60 + 16

Reorder the terms:
16 + 8x + x2 = 60 + 16

Combine like terms: 60 + 16 = 76
16 + 8x + x2 = 76

Factor a perfect square on the left side:
(x + 4)(x + 4) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + 4) equal to 8.717797887 and -8.717797887.

Subproblem 1
x + 4 = 8.717797887

Simplifying
x + 4 = 8.717797887

Reorder the terms:
4 + x = 8.717797887

Solving
4 + x = 8.717797887

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + x = 8.717797887 + -4
x = 8.717797887 + -4

Combine like terms: 8.717797887 + -4 = 4.717797887
x = 4.717797887

Simplifying
x = 4.717797887

Subproblem 2
x + 4 = -8.717797887

Simplifying
x + 4 = -8.717797887

Reorder the terms:
4 + x = -8.717797887

Solving
4 + x = -8.717797887

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + x = -8.717797887 + -4
x = -8.717797887 + -4

Combine like terms: -8.717797887 + -4 = -12.717797887
x = -12.717797887

Simplifying
x = -12.717797887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.717797887, -12.717797887}
Solution
x = {4.717797887, -12.717797887}