2p^2q^2+8pq-24=0

Solution for 2p^2q^2+8pq-24=0 equation:

Simplifying
2p2q2 + 8pq + -24 = 0

Reorder the terms:
-24 + 8pq + 2p2q2 = 0

Solving
-24 + 8pq + 2p2q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4pq + p2q2) = 0

Factor a trinomial.
2((-6 + -1pq)(2 + -1pq)) = 0

Ignore the factor 2.
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 '(2 + -1pq)' equal to zero and attempt to solve:

Simplifying
2 + -1pq = 0

Solving
2 + -1pq = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1pq = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1pq = 0 + -2
-1pq = 0 + -2

Combine like terms: 0 + -2 = -2
-1pq = -2

Divide each side by '-1q'.
p = 2q-1

Simplifying
p = 2q-1
Solution
p = {-6q-1, 2q-1}