4p^2=-15p-9

Solution for 4p^2=-15p-9 equation:

Simplifying
4p2 = -15p + -9

Reorder the terms:
4p2 = -9 + -15p

Solving
4p2 = -9 + -15p

Solving for variable 'p'.

Reorder the terms:
9 + 15p + 4p2 = -9 + -15p + 9 + 15p

Reorder the terms:
9 + 15p + 4p2 = -9 + 9 + -15p + 15p

Combine like terms: -9 + 9 = 0
9 + 15p + 4p2 = 0 + -15p + 15p
9 + 15p + 4p2 = -15p + 15p

Combine like terms: -15p + 15p = 0
9 + 15p + 4p2 = 0

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

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 '(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 = {-3, -0.75}