4p^2+15p=-5+3p

Solution for 4p^2+15p=-5+3p equation:

Simplifying
4p2 + 15p = -5 + 3p

Reorder the terms:
15p + 4p2 = -5 + 3p

Solving
15p + 4p2 = -5 + 3p

Solving for variable 'p'.

Reorder the terms:
5 + 15p + -3p + 4p2 = -5 + 3p + 5 + -3p

Combine like terms: 15p + -3p = 12p
5 + 12p + 4p2 = -5 + 3p + 5 + -3p

Reorder the terms:
5 + 12p + 4p2 = -5 + 5 + 3p + -3p

Combine like terms: -5 + 5 = 0
5 + 12p + 4p2 = 0 + 3p + -3p
5 + 12p + 4p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
5 + 12p + 4p2 = 0

Factor a trinomial.
(5 + 2p)(1 + 2p) = 0

Subproblem 1
Set the factor '(5 + 2p)' equal to zero and attempt to solve:

Simplifying
5 + 2p = 0

Solving
5 + 2p = 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 + 2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2p = 0 + -5
2p = 0 + -5

Combine like terms: 0 + -5 = -5
2p = -5

Divide each side by '2'.
p = -2.5

Simplifying
p = -2.5
Subproblem 2
Set the factor '(1 + 2p)' equal to zero and attempt to solve:

Simplifying
1 + 2p = 0

Solving
1 + 2p = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2p = 0 + -1
2p = 0 + -1

Combine like terms: 0 + -1 = -1
2p = -1

Divide each side by '2'.
p = -0.5

Simplifying
p = -0.5
Solution
p = {-2.5, -0.5}