p^2+12p-40=5

Solution for p^2+12p-40=5 equation:

Simplifying
p2 + 12p + -40 = 5

Reorder the terms:
-40 + 12p + p2 = 5

Solving
-40 + 12p + p2 = 5

Solving for variable 'p'.

Reorder the terms:
-40 + -5 + 12p + p2 = 5 + -5

Combine like terms: -40 + -5 = -45
-45 + 12p + p2 = 5 + -5

Combine like terms: 5 + -5 = 0
-45 + 12p + p2 = 0

Factor a trinomial.
(-15 + -1p)(3 + -1p) = 0

Subproblem 1
Set the factor '(-15 + -1p)' equal to zero and attempt to solve:

Simplifying
-15 + -1p = 0

Solving
-15 + -1p = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1p = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1p = 0 + 15
-1p = 0 + 15

Combine like terms: 0 + 15 = 15
-1p = 15

Divide each side by '-1'.
p = -15

Simplifying
p = -15
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-15, 3}