p^2-13p=-40

Solution for p^2-13p=-40 equation:

Simplifying
p2 + -13p = -40

Reorder the terms:
-13p + p2 = -40

Solving
-13p + p2 = -40

Solving for variable 'p'.

Reorder the terms:
40 + -13p + p2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -13p + p2 = 0

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

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

Simplifying
5 + -1p = 0

Solving
5 + -1p = 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 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Subproblem 2
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
Solution
p = {5, 8}