p(4q-9)+p(6-q)=0

Solution for p(4q-9)+p(6-q)=0 equation:

Simplifying
p(4q + -9) + p(6 + -1q) = 0

Reorder the terms:
p(-9 + 4q) + p(6 + -1q) = 0
(-9 * p + 4q * p) + p(6 + -1q) = 0
(-9p + 4pq) + p(6 + -1q) = 0
-9p + 4pq + (6 * p + -1q * p) = 0
-9p + 4pq + (6p + -1pq) = 0

Reorder the terms:
-9p + 6p + 4pq + -1pq = 0

Combine like terms: -9p + 6p = -3p
-3p + 4pq + -1pq = 0

Combine like terms: 4pq + -1pq = 3pq
-3p + 3pq = 0

Solving
-3p + 3pq = 0

Solving for variable 'p'.

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

Factor out the Greatest Common Factor (GCF), '3p'.
3p(-1 + q) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(-1 + q)' equal to zero and attempt to solve:

Simplifying
-1 + q = 0

Solving
-1 + q = 0

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

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

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

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

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

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

Simplifying
0 = 1 + -1q

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}