p^2+8p+21=6

Solution for p^2+8p+21=6 equation:

Simplifying
p2 + 8p + 21 = 6

Reorder the terms:
21 + 8p + p2 = 6

Solving
21 + 8p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
21 + -6 + 8p + p2 = 6 + -6

Combine like terms: 21 + -6 = 15
15 + 8p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
15 + 8p + p2 = 0

Factor a trinomial.
(5 + p)(3 + p) = 0

Subproblem 1
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
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 = {-5, -3}