(p+2)(p+6)=0

Solution for (p+2)(p+6)=0 equation:

Simplifying
(p + 2)(p + 6) = 0

Reorder the terms:
(2 + p)(p + 6) = 0

Reorder the terms:
(2 + p)(6 + p) = 0

Multiply (2 + p) * (6 + p)
(2(6 + p) + p(6 + p)) = 0
((6 * 2 + p * 2) + p(6 + p)) = 0
((12 + 2p) + p(6 + p)) = 0
(12 + 2p + (6 * p + p * p)) = 0
(12 + 2p + (6p + p2)) = 0

Combine like terms: 2p + 6p = 8p
(12 + 8p + p2) = 0

Solving
12 + 8p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(6 + p)(2 + p) = 0

Subproblem 1
Set the factor '(6 + p)' equal to zero and attempt to solve:

Simplifying
6 + p = 0

Solving
6 + p = 0

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

Add '-6' to each side of the equation.
6 + -6 + p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + p = 0 + -6
p = 0 + -6

Combine like terms: 0 + -6 = -6
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2
Solution
p = {-6, -2}