(6+6r)*q=6+9r

Solution for (6+6r)*q=6+9r equation:

Simplifying
(6 + 6r) * q = 6 + 9r

Reorder the terms for easier multiplication:
q(6 + 6r) = 6 + 9r
(6 * q + 6r * q) = 6 + 9r
(6q + 6qr) = 6 + 9r

Solving
6q + 6qr = 6 + 9r

Solving for variable 'q'.

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

Reorder the terms:
-6 + 6q + 6qr + -9r = 6 + 9r + -6 + -9r

Reorder the terms:
-6 + 6q + 6qr + -9r = 6 + -6 + 9r + -9r

Combine like terms: 6 + -6 = 0
-6 + 6q + 6qr + -9r = 0 + 9r + -9r
-6 + 6q + 6qr + -9r = 9r + -9r

Combine like terms: 9r + -9r = 0
-6 + 6q + 6qr + -9r = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 2q + 2qr + -3r) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 2q + 2qr + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + 2q + 2qr + -3r = 0

Solving
-2 + 2q + 2qr + -3r = 0

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

Add '2' to each side of the equation.
-2 + 2q + 2qr + 2 + -3r = 0 + 2

Reorder the terms:
-2 + 2 + 2q + 2qr + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2q + 2qr + -3r = 0 + 2
2q + 2qr + -3r = 0 + 2

Combine like terms: 0 + 2 = 2
2q + 2qr + -3r = 2

Add '3r' to each side of the equation.
2q + 2qr + -3r + 3r = 2 + 3r

Combine like terms: -3r + 3r = 0
2q + 2qr + 0 = 2 + 3r
2q + 2qr = 2 + 3r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.