p^2+12*p+21=-6

Solution for p^2+12*p+21=-6 equation:

Simplifying
p2 + 12p + 21 = -6

Reorder the terms:
21 + 12p + p2 = -6

Solving
21 + 12p + p2 = -6

Solving for variable 'p'.

Reorder the terms:
21 + 6 + 12p + p2 = -6 + 6

Combine like terms: 21 + 6 = 27
27 + 12p + p2 = -6 + 6

Combine like terms: -6 + 6 = 0
27 + 12p + p2 = 0

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

Subproblem 1
Set the factor '(9 + p)' equal to zero and attempt to solve:

Simplifying
9 + p = 0

Solving
9 + p = 0

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

Add '-9' to each side of the equation.
9 + -9 + p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + p = 0 + -9
p = 0 + -9

Combine like terms: 0 + -9 = -9
p = -9

Simplifying
p = -9
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 = {-9, -3}