4x^2-45=5x^2+18x

Solution for 4x^2-45=5x^2+18x equation:

Simplifying
4x2 + -45 = 5x2 + 18x

Reorder the terms:
-45 + 4x2 = 5x2 + 18x

Reorder the terms:
-45 + 4x2 = 18x + 5x2

Solving
-45 + 4x2 = 18x + 5x2

Solving for variable 'x'.

Reorder the terms:
-45 + -18x + 4x2 + -5x2 = 18x + 5x2 + -18x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-45 + -18x + -1x2 = 18x + 5x2 + -18x + -5x2

Reorder the terms:
-45 + -18x + -1x2 = 18x + -18x + 5x2 + -5x2

Combine like terms: 18x + -18x = 0
-45 + -18x + -1x2 = 0 + 5x2 + -5x2
-45 + -18x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-45 + -18x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 18x + x2) = 0

Factor a trinomial.
-1((15 + x)(3 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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 = 0 + -15

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

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

Simplifying
x = -15
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-15, -3}