360=3x(5x+60)

Solution for 360=3x(5x+60) equation:

Simplifying
360 = 3x(5x + 60)

Reorder the terms:
360 = 3x(60 + 5x)
360 = (60 * 3x + 5x * 3x)
360 = (180x + 15x2)

Solving
360 = 180x + 15x2

Solving for variable 'x'.

Reorder the terms:
360 + -180x + -15x2 = 180x + -180x + 15x2 + -15x2

Combine like terms: 180x + -180x = 0
360 + -180x + -15x2 = 0 + 15x2 + -15x2
360 + -180x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
360 + -180x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(24 + -12x + -1x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(24 + -12x + -1x2)' equal to zero and attempt to solve:

Simplifying
24 + -12x + -1x2 = 0

Solving
24 + -12x + -1x2 = 0

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

Divide each side by '-1'.
-24 + 12x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 12x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 12x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 12x + x2 = 0 + 24
12x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
12x + x2 = 24

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 24 + 36

Reorder the terms:
36 + 12x + x2 = 24 + 36

Combine like terms: 24 + 36 = 60
36 + 12x + x2 = 60

Factor a perfect square on the left side:
(x + 6)(x + 6) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 6) equal to 7.745966692 and -7.745966692.

Subproblem 1
x + 6 = 7.745966692

Simplifying
x + 6 = 7.745966692

Reorder the terms:
6 + x = 7.745966692

Solving
6 + x = 7.745966692

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 7.745966692 + -6

Combine like terms: 6 + -6 = 0
0 + x = 7.745966692 + -6
x = 7.745966692 + -6

Combine like terms: 7.745966692 + -6 = 1.745966692
x = 1.745966692

Simplifying
x = 1.745966692

Subproblem 2
x + 6 = -7.745966692

Simplifying
x + 6 = -7.745966692

Reorder the terms:
6 + x = -7.745966692

Solving
6 + x = -7.745966692

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -7.745966692 + -6

Combine like terms: 6 + -6 = 0
0 + x = -7.745966692 + -6
x = -7.745966692 + -6

Combine like terms: -7.745966692 + -6 = -13.745966692
x = -13.745966692

Simplifying
x = -13.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.745966692, -13.745966692}
Solution
x = {1.745966692, -13.745966692}