Simplifying
-2p2 + 28p + -66 = 0

Reorder the terms:
-66 + 28p + -2p2 = 0

Solving
-66 + 28p + -2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 14p + -1p2) = 0

Factor a trinomial.
2((-11 + p)(3 + -1p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + p)' equal to zero and attempt to solve:

Simplifying
-11 + p = 0

Solving
-11 + p = 0

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

Add '11' to each side of the equation.
-11 + 11 + p = 0 + 11

Combine like terms: -11 + 11 = 0
0 + p = 0 + 11
p = 0 + 11

Combine like terms: 0 + 11 = 11
p = 11

Simplifying
p = 11
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 = {11, 3}