6q^2-3q=5q^2-5q+48

Solution for 6q^2-3q=5q^2-5q+48 equation:

Simplifying
6q2 + -3q = 5q2 + -5q + 48

Reorder the terms:
-3q + 6q2 = 5q2 + -5q + 48

Reorder the terms:
-3q + 6q2 = 48 + -5q + 5q2

Solving
-3q + 6q2 = 48 + -5q + 5q2

Solving for variable 'q'.

Reorder the terms:
-48 + -3q + 5q + 6q2 + -5q2 = 48 + -5q + 5q2 + -48 + 5q + -5q2

Combine like terms: -3q + 5q = 2q
-48 + 2q + 6q2 + -5q2 = 48 + -5q + 5q2 + -48 + 5q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-48 + 2q + 1q2 = 48 + -5q + 5q2 + -48 + 5q + -5q2

Reorder the terms:
-48 + 2q + 1q2 = 48 + -48 + -5q + 5q + 5q2 + -5q2

Combine like terms: 48 + -48 = 0
-48 + 2q + 1q2 = 0 + -5q + 5q + 5q2 + -5q2
-48 + 2q + 1q2 = -5q + 5q + 5q2 + -5q2

Combine like terms: -5q + 5q = 0
-48 + 2q + 1q2 = 0 + 5q2 + -5q2
-48 + 2q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-48 + 2q + 1q2 = 0

Factor a trinomial.
(-8 + -1q)(6 + -1q) = 0

Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve:

Simplifying
-8 + -1q = 0

Solving
-8 + -1q = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1q = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1q = 0 + 8
-1q = 0 + 8

Combine like terms: 0 + 8 = 8
-1q = 8

Divide each side by '-1'.
q = -8

Simplifying
q = -8
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 = {-8, 6}