-4p^2-17p-15=0

Solution for -4p^2-17p-15=0 equation:

Simplifying
-4p2 + -17p + -15 = 0

Reorder the terms:
-15 + -17p + -4p2 = 0

Solving
-15 + -17p + -4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 17p + 4p2) = 0

Factor a trinomial.
-1((3 + p)(5 + 4p)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

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

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

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(5 + 4p)' equal to zero and attempt to solve:

Simplifying
5 + 4p = 0

Solving
5 + 4p = 0

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

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

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

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

Divide each side by '4'.
p = -1.25

Simplifying
p = -1.25
Solution
p = {-3, -1.25}