6q^2-6q=5q^2-9q+18

Solution for 6q^2-6q=5q^2-9q+18 equation:

Simplifying
6q2 + -6q = 5q2 + -9q + 18

Reorder the terms:
-6q + 6q2 = 5q2 + -9q + 18

Reorder the terms:
-6q + 6q2 = 18 + -9q + 5q2

Solving
-6q + 6q2 = 18 + -9q + 5q2

Solving for variable 'q'.

Reorder the terms:
-18 + -6q + 9q + 6q2 + -5q2 = 18 + -9q + 5q2 + -18 + 9q + -5q2

Combine like terms: -6q + 9q = 3q
-18 + 3q + 6q2 + -5q2 = 18 + -9q + 5q2 + -18 + 9q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-18 + 3q + 1q2 = 18 + -9q + 5q2 + -18 + 9q + -5q2

Reorder the terms:
-18 + 3q + 1q2 = 18 + -18 + -9q + 9q + 5q2 + -5q2

Combine like terms: 18 + -18 = 0
-18 + 3q + 1q2 = 0 + -9q + 9q + 5q2 + -5q2
-18 + 3q + 1q2 = -9q + 9q + 5q2 + -5q2

Combine like terms: -9q + 9q = 0
-18 + 3q + 1q2 = 0 + 5q2 + -5q2
-18 + 3q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-18 + 3q + 1q2 = 0

Factor a trinomial.
(-6 + -1q)(3 + -1q) = 0

Subproblem 1
Set the factor '(-6 + -1q)' equal to zero and attempt to solve:

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1q = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1q = 0 + 6
-1q = 0 + 6

Combine like terms: 0 + 6 = 6
-1q = 6

Divide each side by '-1'.
q = -6

Simplifying
q = -6
Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

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

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

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

Simplifying
q = 3
Solution
q = {-6, 3}