6q^2-4q=5q^2-7q

Solution for 6q^2-4q=5q^2-7q equation:

Simplifying
6q2 + -4q = 5q2 + -7q

Reorder the terms:
-4q + 6q2 = 5q2 + -7q

Reorder the terms:
-4q + 6q2 = -7q + 5q2

Solving
-4q + 6q2 = -7q + 5q2

Solving for variable 'q'.

Reorder the terms:
-4q + 7q + 6q2 + -5q2 = -7q + 5q2 + 7q + -5q2

Combine like terms: -4q + 7q = 3q
3q + 6q2 + -5q2 = -7q + 5q2 + 7q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
3q + 1q2 = -7q + 5q2 + 7q + -5q2

Reorder the terms:
3q + 1q2 = -7q + 7q + 5q2 + -5q2

Combine like terms: -7q + 7q = 0
3q + 1q2 = 0 + 5q2 + -5q2
3q + 1q2 = 5q2 + -5q2

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

Factor out the Greatest Common Factor (GCF), 'q'.
q(3 + q) = 0

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 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 + q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + q = 0 + -3
q = 0 + -3

Combine like terms: 0 + -3 = -3
q = -3

Simplifying
q = -3
Solution
q = {0, -3}