6q^2-3q=5q^2-5q+24

Solution for 6q^2-3q=5q^2-5q+24 equation:

Simplifying
6q2 + -3q = 5q2 + -5q + 24

Reorder the terms:
-3q + 6q2 = 5q2 + -5q + 24

Reorder the terms:
-3q + 6q2 = 24 + -5q + 5q2

Solving
-3q + 6q2 = 24 + -5q + 5q2

Solving for variable 'q'.

Reorder the terms:
-24 + -3q + 5q + 6q2 + -5q2 = 24 + -5q + 5q2 + -24 + 5q + -5q2

Combine like terms: -3q + 5q = 2q
-24 + 2q + 6q2 + -5q2 = 24 + -5q + 5q2 + -24 + 5q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-24 + 2q + 1q2 = 24 + -5q + 5q2 + -24 + 5q + -5q2

Reorder the terms:
-24 + 2q + 1q2 = 24 + -24 + -5q + 5q + 5q2 + -5q2

Combine like terms: 24 + -24 = 0
-24 + 2q + 1q2 = 0 + -5q + 5q + 5q2 + -5q2
-24 + 2q + 1q2 = -5q + 5q + 5q2 + -5q2

Combine like terms: -5q + 5q = 0
-24 + 2q + 1q2 = 0 + 5q2 + -5q2
-24 + 2q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-24 + 2q + 1q2 = 0

Factor a trinomial.
(-6 + -1q)(4 + -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 '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {-6, 4}