4p^2=-23p-15

Solution for 4p^2=-23p-15 equation:

Simplifying
4p2 = -23p + -15

Reorder the terms:
4p2 = -15 + -23p

Solving
4p2 = -15 + -23p

Solving for variable 'p'.

Reorder the terms:
15 + 23p + 4p2 = -15 + -23p + 15 + 23p

Reorder the terms:
15 + 23p + 4p2 = -15 + 15 + -23p + 23p

Combine like terms: -15 + 15 = 0
15 + 23p + 4p2 = 0 + -23p + 23p
15 + 23p + 4p2 = -23p + 23p

Combine like terms: -23p + 23p = 0
15 + 23p + 4p2 = 0

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

Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 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 + p = 0 + -5

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

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

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

Simplifying
3 + 4p = 0

Solving
3 + 4p = 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 + 4p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4p = 0 + -3
4p = 0 + -3

Combine like terms: 0 + -3 = -3
4p = -3

Divide each side by '4'.
p = -0.75

Simplifying
p = -0.75
Solution
p = {-5, -0.75}