18x^2+18x=360x+72

Solution for 18x^2+18x=360x+72 equation:

Simplifying
18x2 + 18x = 360x + 72

Reorder the terms:
18x + 18x2 = 360x + 72

Reorder the terms:
18x + 18x2 = 72 + 360x

Solving
18x + 18x2 = 72 + 360x

Solving for variable 'x'.

Reorder the terms:
-72 + 18x + -360x + 18x2 = 72 + 360x + -72 + -360x

Combine like terms: 18x + -360x = -342x
-72 + -342x + 18x2 = 72 + 360x + -72 + -360x

Reorder the terms:
-72 + -342x + 18x2 = 72 + -72 + 360x + -360x

Combine like terms: 72 + -72 = 0
-72 + -342x + 18x2 = 0 + 360x + -360x
-72 + -342x + 18x2 = 360x + -360x

Combine like terms: 360x + -360x = 0
-72 + -342x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(-4 + -19x + x2) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-4 + -19x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -19x + x2 = 0

Solving
-4 + -19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -19x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -19x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -19x + x2 = 0 + 4
-19x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-19x + x2 = 4

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 4 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 4 + 90.25

Combine like terms: 4 + 90.25 = 94.25
90.25 + -19x + x2 = 94.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 94.25

Calculate the square root of the right side: 9.708243919

Break this problem into two subproblems by setting 
(x + -9.5) equal to 9.708243919 and -9.708243919.

Subproblem 1
x + -9.5 = 9.708243919

Simplifying
x + -9.5 = 9.708243919

Reorder the terms:
-9.5 + x = 9.708243919

Solving
-9.5 + x = 9.708243919

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 9.708243919 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 9.708243919 + 9.5
x = 9.708243919 + 9.5

Combine like terms: 9.708243919 + 9.5 = 19.208243919
x = 19.208243919

Simplifying
x = 19.208243919

Subproblem 2
x + -9.5 = -9.708243919

Simplifying
x + -9.5 = -9.708243919

Reorder the terms:
-9.5 + x = -9.708243919

Solving
-9.5 + x = -9.708243919

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -9.708243919 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -9.708243919 + 9.5
x = -9.708243919 + 9.5

Combine like terms: -9.708243919 + 9.5 = -0.208243919
x = -0.208243919

Simplifying
x = -0.208243919

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.208243919, -0.208243919}
Solution
x = {19.208243919, -0.208243919}