3x(5x+36)=180

Solution for 3x(5x+36)=180 equation:

Simplifying
3x(5x + 36) = 180

Reorder the terms:
3x(36 + 5x) = 180
(36 * 3x + 5x * 3x) = 180
(108x + 15x2) = 180

Solving
108x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 108x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 108x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 36x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-60 + 36x + 5x2)' equal to zero and attempt to solve:

Simplifying
-60 + 36x + 5x2 = 0

Solving
-60 + 36x + 5x2 = 0

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

Divide each side by '5'.
-12 + 7.2x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 7.2x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 7.2x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7.2x + x2 = 0 + 12
7.2x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
7.2x + x2 = 12

The x term is 7.2x.  Take half its coefficient (3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
7.2x + 12.96 + x2 = 12 + 12.96

Reorder the terms:
12.96 + 7.2x + x2 = 12 + 12.96

Combine like terms: 12 + 12.96 = 24.96
12.96 + 7.2x + x2 = 24.96

Factor a perfect square on the left side:
(x + 3.6)(x + 3.6) = 24.96

Calculate the square root of the right side: 4.995998399

Break this problem into two subproblems by setting 
(x + 3.6) equal to 4.995998399 and -4.995998399.

Subproblem 1
x + 3.6 = 4.995998399

Simplifying
x + 3.6 = 4.995998399

Reorder the terms:
3.6 + x = 4.995998399

Solving
3.6 + x = 4.995998399

Solving for variable 'x'.

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

Add '-3.6' to each side of the equation.
3.6 + -3.6 + x = 4.995998399 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + x = 4.995998399 + -3.6
x = 4.995998399 + -3.6

Combine like terms: 4.995998399 + -3.6 = 1.395998399
x = 1.395998399

Simplifying
x = 1.395998399

Subproblem 2
x + 3.6 = -4.995998399

Simplifying
x + 3.6 = -4.995998399

Reorder the terms:
3.6 + x = -4.995998399

Solving
3.6 + x = -4.995998399

Solving for variable 'x'.

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

Add '-3.6' to each side of the equation.
3.6 + -3.6 + x = -4.995998399 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + x = -4.995998399 + -3.6
x = -4.995998399 + -3.6

Combine like terms: -4.995998399 + -3.6 = -8.595998399
x = -8.595998399

Simplifying
x = -8.595998399

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.395998399, -8.595998399}
Solution
x = {1.395998399, -8.595998399}