p^2-5pq-24q^2=

Solution for p^2-5pq-24q^2= equation:

Simplifying
p2 + -5pq + -24q2 = 0

Reorder the terms:
-5pq + p2 + -24q2 = 0

Solving
-5pq + p2 + -24q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(p + -8q)(p + 3q) = 0

Subproblem 1
Set the factor '(p + -8q)' equal to zero and attempt to solve:

Simplifying
p + -8q = 0

Solving
p + -8q = 0

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

Add '8q' to each side of the equation.
p + -8q + 8q = 0 + 8q

Combine like terms: -8q + 8q = 0
p + 0 = 0 + 8q
p = 0 + 8q
Remove the zero:
p = 8q

Simplifying
p = 8q
Subproblem 2
Set the factor '(p + 3q)' equal to zero and attempt to solve:

Simplifying
p + 3q = 0

Solving
p + 3q = 0

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

Add '-3q' to each side of the equation.
p + 3q + -3q = 0 + -3q

Combine like terms: 3q + -3q = 0
p + 0 = 0 + -3q
p = 0 + -3q
Remove the zero:
p = -3q

Simplifying
p = -3q
Solution
p = {8q, -3q}