5p^2=-24p-16

Solution for 5p^2=-24p-16 equation:

Simplifying
5p2 = -24p + -16

Reorder the terms:
5p2 = -16 + -24p

Solving
5p2 = -16 + -24p

Solving for variable 'p'.

Reorder the terms:
16 + 24p + 5p2 = -16 + -24p + 16 + 24p

Reorder the terms:
16 + 24p + 5p2 = -16 + 16 + -24p + 24p

Combine like terms: -16 + 16 = 0
16 + 24p + 5p2 = 0 + -24p + 24p
16 + 24p + 5p2 = -24p + 24p

Combine like terms: -24p + 24p = 0
16 + 24p + 5p2 = 0

Factor a trinomial.
(4 + p)(4 + 5p) = 0

Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 0

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

Add '-4' to each side of the equation.
4 + -4 + p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + p = 0 + -4
p = 0 + -4

Combine like terms: 0 + -4 = -4
p = -4

Simplifying
p = -4
Subproblem 2
Set the factor '(4 + 5p)' equal to zero and attempt to solve:

Simplifying
4 + 5p = 0

Solving
4 + 5p = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5p = 0 + -4
5p = 0 + -4

Combine like terms: 0 + -4 = -4
5p = -4

Divide each side by '5'.
p = -0.8

Simplifying
p = -0.8
Solution
p = {-4, -0.8}