4x^2-72=5x^2+18x

Solution for 4x^2-72=5x^2+18x equation:

Simplifying
4x2 + -72 = 5x2 + 18x

Reorder the terms:
-72 + 4x2 = 5x2 + 18x

Reorder the terms:
-72 + 4x2 = 18x + 5x2

Solving
-72 + 4x2 = 18x + 5x2

Solving for variable 'x'.

Reorder the terms:
-72 + -18x + 4x2 + -5x2 = 18x + 5x2 + -18x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-72 + -18x + -1x2 = 18x + 5x2 + -18x + -5x2

Reorder the terms:
-72 + -18x + -1x2 = 18x + -18x + 5x2 + -5x2

Combine like terms: 18x + -18x = 0
-72 + -18x + -1x2 = 0 + 5x2 + -5x2
-72 + -18x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-72 + -18x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(72 + 18x + x2) = 0

Factor a trinomial.
-1((12 + x)(6 + x)) = 0

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

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-12, -6}