5x(x+30)=720

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Solution for 5x(x+30)=720 equation: 


Simplifying
5x(x + 30) = 720

Reorder the terms:
5x(30 + x) = 720
(30 * 5x + x * 5x) = 720
(150x + 5x2) = 720

Solving
150x + 5x2 = 720

Solving for variable 'x'.

Reorder the terms:
-720 + 150x + 5x2 = 720 + -720

Combine like terms: 720 + -720 = 0
-720 + 150x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-144 + 30x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-144 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-144 + 30x + x2 = 0

Solving
-144 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 30x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 30x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 30x + x2 = 0 + 144
30x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
30x + x2 = 144

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 144 + 225

Reorder the terms:
225 + 30x + x2 = 144 + 225

Combine like terms: 144 + 225 = 369
225 + 30x + x2 = 369

Factor a perfect square on the left side:
(x + 15)(x + 15) = 369

Calculate the square root of the right side: 19.209372712

Break this problem into two subproblems by setting 
(x + 15) equal to 19.209372712 and -19.209372712.


Subproblem 1
x + 15 = 19.209372712

Simplifying
x + 15 = 19.209372712

Reorder the terms:
15 + x = 19.209372712

Solving
15 + x = 19.209372712

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 19.209372712 + -15

Combine like terms: 15 + -15 = 0
0 + x = 19.209372712 + -15
x = 19.209372712 + -15

Combine like terms: 19.209372712 + -15 = 4.209372712
x = 4.209372712

Simplifying
x = 4.209372712


Subproblem 2
x + 15 = -19.209372712

Simplifying
x + 15 = -19.209372712

Reorder the terms:
15 + x = -19.209372712

Solving
15 + x = -19.209372712

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -19.209372712 + -15

Combine like terms: 15 + -15 = 0
0 + x = -19.209372712 + -15
x = -19.209372712 + -15

Combine like terms: -19.209372712 + -15 = -34.209372712
x = -34.209372712

Simplifying
x = -34.209372712


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.209372712, -34.209372712}
Solution
x = {4.209372712, -34.209372712}

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