5x(3x+20)=360

Solution for 5x(3x+20)=360 equation:

Simplifying
5x(3x + 20) = 360

Reorder the terms:
5x(20 + 3x) = 360
(20 * 5x + 3x * 5x) = 360
(100x + 15x2) = 360

Solving
100x + 15x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 100x + 15x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 100x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-72 + 20x + 3x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-72 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-72 + 20x + 3x2 = 0

Solving
-72 + 20x + 3x2 = 0

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

Divide each side by '3'.
-24 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 6.666666667x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 6.666666667x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 6.666666667x + x2 = 0 + 24
6.666666667x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
6.666666667x + x2 = 24

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 24 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 24 + 11.11111112

Combine like terms: 24 + 11.11111112 = 35.11111112
11.11111112 + 6.666666667x + x2 = 35.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 35.11111112

Calculate the square root of the right side: 5.925462946

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 5.925462946 and -5.925462946.

Subproblem 1
x + 3.333333334 = 5.925462946

Simplifying
x + 3.333333334 = 5.925462946

Reorder the terms:
3.333333334 + x = 5.925462946

Solving
3.333333334 + x = 5.925462946

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 5.925462946 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 5.925462946 + -3.333333334
x = 5.925462946 + -3.333333334

Combine like terms: 5.925462946 + -3.333333334 = 2.592129612
x = 2.592129612

Simplifying
x = 2.592129612

Subproblem 2
x + 3.333333334 = -5.925462946

Simplifying
x + 3.333333334 = -5.925462946

Reorder the terms:
3.333333334 + x = -5.925462946

Solving
3.333333334 + x = -5.925462946

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -5.925462946 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -5.925462946 + -3.333333334
x = -5.925462946 + -3.333333334

Combine like terms: -5.925462946 + -3.333333334 = -9.25879628
x = -9.25879628

Simplifying
x = -9.25879628

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.592129612, -9.25879628}
Solution
x = {2.592129612, -9.25879628}