40=P^2-3P

Solution for 40=P^2-3P equation:

Simplifying
40 = P2 + -3P

Reorder the terms:
40 = -3P + P2

Solving
40 = -3P + P2

Solving for variable 'P'.

Reorder the terms:
40 + 3P + -1P2 = -3P + 3P + P2 + -1P2

Combine like terms: -3P + 3P = 0
40 + 3P + -1P2 = 0 + P2 + -1P2
40 + 3P + -1P2 = P2 + -1P2

Combine like terms: P2 + -1P2 = 0
40 + 3P + -1P2 = 0

Factor a trinomial.
(8 + -1P)(5 + P) = 0

Subproblem 1
Set the factor '(8 + -1P)' equal to zero and attempt to solve:

Simplifying
8 + -1P = 0

Solving
8 + -1P = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1P = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1P = 0 + -8
-1P = 0 + -8

Combine like terms: 0 + -8 = -8
-1P = -8

Divide each side by '-1'.
P = 8

Simplifying
P = 8
Subproblem 2
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
Solution
P = {8, -5}