x^2+18=5x^2-6x

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Solution for x^2+18=5x^2-6x equation: 


Simplifying
x2 + 18 = 5x2 + -6x

Reorder the terms:
18 + x2 = 5x2 + -6x

Reorder the terms:
18 + x2 = -6x + 5x2

Solving
18 + x2 = -6x + 5x2

Solving for variable 'x'.

Reorder the terms:
18 + 6x + x2 + -5x2 = -6x + 5x2 + 6x + -5x2

Combine like terms: x2 + -5x2 = -4x2
18 + 6x + -4x2 = -6x + 5x2 + 6x + -5x2

Reorder the terms:
18 + 6x + -4x2 = -6x + 6x + 5x2 + -5x2

Combine like terms: -6x + 6x = 0
18 + 6x + -4x2 = 0 + 5x2 + -5x2
18 + 6x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
18 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 3x + -2x2) = 0

Factor a trinomial.
2((3 + -1x)(3 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {3, -1.5}

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