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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}
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