5p^2q^2+25pq-30=0

Solution for 5p^2q^2+25pq-30=0 equation:

Simplifying
5p2q2 + 25pq + -30 = 0

Reorder the terms:
-30 + 25pq + 5p2q2 = 0

Solving
-30 + 25pq + 5p2q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 5pq + p2q2) = 0

Factor a trinomial.
5((-6 + -1pq)(1 + -1pq)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1pq)' equal to zero and attempt to solve:

Simplifying
-6 + -1pq = 0

Solving
-6 + -1pq = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1pq = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1pq = 0 + 6
-1pq = 0 + 6

Combine like terms: 0 + 6 = 6
-1pq = 6

Divide each side by '-1q'.
p = -6q-1

Simplifying
p = -6q-1
Subproblem 2
Set the factor '(1 + -1pq)' equal to zero and attempt to solve:

Simplifying
1 + -1pq = 0

Solving
1 + -1pq = 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 + -1pq = 0 + -1

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

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

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

Simplifying
p = q-1
Solution
p = {-6q-1, q-1}