5x(3x+60)=360

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


Simplifying
5x(3x + 60) = 360

Reorder the terms:
5x(60 + 3x) = 360
(60 * 5x + 3x * 5x) = 360
(300x + 15x2) = 360

Solving
300x + 15x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 300x + 15x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 300x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-24 + 20x + x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-24 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 20x + x2 = 0

Solving
-24 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 20x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 20x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 20x + x2 = 0 + 24
20x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
20x + x2 = 24

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 24 + 100

Reorder the terms:
100 + 20x + x2 = 24 + 100

Combine like terms: 24 + 100 = 124
100 + 20x + x2 = 124

Factor a perfect square on the left side:
(x + 10)(x + 10) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + 10) equal to 11.135528726 and -11.135528726.


Subproblem 1
x + 10 = 11.135528726

Simplifying
x + 10 = 11.135528726

Reorder the terms:
10 + x = 11.135528726

Solving
10 + x = 11.135528726

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 11.135528726 + -10

Combine like terms: 10 + -10 = 0
0 + x = 11.135528726 + -10
x = 11.135528726 + -10

Combine like terms: 11.135528726 + -10 = 1.135528726
x = 1.135528726

Simplifying
x = 1.135528726


Subproblem 2
x + 10 = -11.135528726

Simplifying
x + 10 = -11.135528726

Reorder the terms:
10 + x = -11.135528726

Solving
10 + x = -11.135528726

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -11.135528726 + -10

Combine like terms: 10 + -10 = 0
0 + x = -11.135528726 + -10
x = -11.135528726 + -10

Combine like terms: -11.135528726 + -10 = -21.135528726
x = -21.135528726

Simplifying
x = -21.135528726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.135528726, -21.135528726}
Solution
x = {1.135528726, -21.135528726}

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