6q^2-3q=5q^2-6q+54

Solution for 6q^2-3q=5q^2-6q+54 equation:

Simplifying
6q2 + -3q = 5q2 + -6q + 54

Reorder the terms:
-3q + 6q2 = 5q2 + -6q + 54

Reorder the terms:
-3q + 6q2 = 54 + -6q + 5q2

Solving
-3q + 6q2 = 54 + -6q + 5q2

Solving for variable 'q'.

Reorder the terms:
-54 + -3q + 6q + 6q2 + -5q2 = 54 + -6q + 5q2 + -54 + 6q + -5q2

Combine like terms: -3q + 6q = 3q
-54 + 3q + 6q2 + -5q2 = 54 + -6q + 5q2 + -54 + 6q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-54 + 3q + 1q2 = 54 + -6q + 5q2 + -54 + 6q + -5q2

Reorder the terms:
-54 + 3q + 1q2 = 54 + -54 + -6q + 6q + 5q2 + -5q2

Combine like terms: 54 + -54 = 0
-54 + 3q + 1q2 = 0 + -6q + 6q + 5q2 + -5q2
-54 + 3q + 1q2 = -6q + 6q + 5q2 + -5q2

Combine like terms: -6q + 6q = 0
-54 + 3q + 1q2 = 0 + 5q2 + -5q2
-54 + 3q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-54 + 3q + 1q2 = 0

Factor a trinomial.
(-9 + -1q)(6 + -1q) = 0

Subproblem 1
Set the factor '(-9 + -1q)' equal to zero and attempt to solve:

Simplifying
-9 + -1q = 0

Solving
-9 + -1q = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1q = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1q = 0 + 9
-1q = 0 + 9

Combine like terms: 0 + 9 = 9
-1q = 9

Divide each side by '-1'.
q = -9

Simplifying
q = -9
Subproblem 2
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
Solution
q = {-9, 6}