6q^2+4q=5q^2-2q+27

Solution for 6q^2+4q=5q^2-2q+27 equation:

Simplifying
6q2 + 4q = 5q2 + -2q + 27

Reorder the terms:
4q + 6q2 = 5q2 + -2q + 27

Reorder the terms:
4q + 6q2 = 27 + -2q + 5q2

Solving
4q + 6q2 = 27 + -2q + 5q2

Solving for variable 'q'.

Reorder the terms:
-27 + 4q + 2q + 6q2 + -5q2 = 27 + -2q + 5q2 + -27 + 2q + -5q2

Combine like terms: 4q + 2q = 6q
-27 + 6q + 6q2 + -5q2 = 27 + -2q + 5q2 + -27 + 2q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-27 + 6q + 1q2 = 27 + -2q + 5q2 + -27 + 2q + -5q2

Reorder the terms:
-27 + 6q + 1q2 = 27 + -27 + -2q + 2q + 5q2 + -5q2

Combine like terms: 27 + -27 = 0
-27 + 6q + 1q2 = 0 + -2q + 2q + 5q2 + -5q2
-27 + 6q + 1q2 = -2q + 2q + 5q2 + -5q2

Combine like terms: -2q + 2q = 0
-27 + 6q + 1q2 = 0 + 5q2 + -5q2
-27 + 6q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-27 + 6q + 1q2 = 0

Factor a trinomial.
(-9 + -1q)(3 + -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 '(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 = {-9, 3}