4p^2q^2+20pq-24=

Solution for 4p^2q^2+20pq-24= equation:

Simplifying
4p2q2 + 20pq + -24 = 0

Reorder the terms:
-24 + 20pq + 4p2q2 = 0

Solving
-24 + 20pq + 4p2q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 5pq + p2q2) = 0

Factor a trinomial.
4((-6 + -1pq)(1 + -1pq)) = 0

Ignore the factor 4.
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}