p^2+20p+90=-6

Solution for p^2+20p+90=-6 equation:

Simplifying
p2 + 20p + 90 = -6

Reorder the terms:
90 + 20p + p2 = -6

Solving
90 + 20p + p2 = -6

Solving for variable 'p'.

Reorder the terms:
90 + 6 + 20p + p2 = -6 + 6

Combine like terms: 90 + 6 = 96
96 + 20p + p2 = -6 + 6

Combine like terms: -6 + 6 = 0
96 + 20p + p2 = 0

Factor a trinomial.
(12 + p)(8 + p) = 0

Subproblem 1
Set the factor '(12 + p)' equal to zero and attempt to solve:

Simplifying
12 + p = 0

Solving
12 + p = 0

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

Add '-12' to each side of the equation.
12 + -12 + p = 0 + -12

Combine like terms: 12 + -12 = 0
0 + p = 0 + -12
p = 0 + -12

Combine like terms: 0 + -12 = -12
p = -12

Simplifying
p = -12
Subproblem 2
Set the factor '(8 + p)' equal to zero and attempt to solve:

Simplifying
8 + p = 0

Solving
8 + p = 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 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
Solution
p = {-12, -8}