6q^2+2q=5q^2-2q+12

Solution for 6q^2+2q=5q^2-2q+12 equation:

Simplifying
6q2 + 2q = 5q2 + -2q + 12

Reorder the terms:
2q + 6q2 = 5q2 + -2q + 12

Reorder the terms:
2q + 6q2 = 12 + -2q + 5q2

Solving
2q + 6q2 = 12 + -2q + 5q2

Solving for variable 'q'.

Reorder the terms:
-12 + 2q + 2q + 6q2 + -5q2 = 12 + -2q + 5q2 + -12 + 2q + -5q2

Combine like terms: 2q + 2q = 4q
-12 + 4q + 6q2 + -5q2 = 12 + -2q + 5q2 + -12 + 2q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-12 + 4q + 1q2 = 12 + -2q + 5q2 + -12 + 2q + -5q2

Reorder the terms:
-12 + 4q + 1q2 = 12 + -12 + -2q + 2q + 5q2 + -5q2

Combine like terms: 12 + -12 = 0
-12 + 4q + 1q2 = 0 + -2q + 2q + 5q2 + -5q2
-12 + 4q + 1q2 = -2q + 2q + 5q2 + -5q2

Combine like terms: -2q + 2q = 0
-12 + 4q + 1q2 = 0 + 5q2 + -5q2
-12 + 4q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-12 + 4q + 1q2 = 0

Factor a trinomial.
(-6 + -1q)(2 + -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 '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

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