15-2P=-6+3P^2

Solution for 15-2P=-6+3P^2 equation:

Simplifying
15 + -2P = -6 + 3P2

Solving
15 + -2P = -6 + 3P2

Solving for variable 'P'.

Reorder the terms:
15 + 6 + -2P + -3P2 = -6 + 3P2 + 6 + -3P2

Combine like terms: 15 + 6 = 21
21 + -2P + -3P2 = -6 + 3P2 + 6 + -3P2

Reorder the terms:
21 + -2P + -3P2 = -6 + 6 + 3P2 + -3P2

Combine like terms: -6 + 6 = 0
21 + -2P + -3P2 = 0 + 3P2 + -3P2
21 + -2P + -3P2 = 3P2 + -3P2

Combine like terms: 3P2 + -3P2 = 0
21 + -2P + -3P2 = 0

Factor a trinomial.
(7 + -3P)(3 + P) = 0

Subproblem 1
Set the factor '(7 + -3P)' equal to zero and attempt to solve:

Simplifying
7 + -3P = 0

Solving
7 + -3P = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3P = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3P = 0 + -7
-3P = 0 + -7

Combine like terms: 0 + -7 = -7
-3P = -7

Divide each side by '-3'.
P = 2.333333333

Simplifying
P = 2.333333333
Subproblem 2
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
Solution
P = {2.333333333, -3}