3x^2+36x-72=0

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Solution for 3x^2+36x-72=0 equation: 


Simplifying
3x2 + 36x + -72 = 0

Reorder the terms:
-72 + 36x + 3x2 = 0

Solving
-72 + 36x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 12x + x2) = 0

Ignore the factor 3.

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

Simplifying
-24 + 12x + x2 = 0

Solving
-24 + 12x + x2 = 0

Begin completing the square.

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}

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