p(p+18)=-77

Solution for p(p+18)=-77 equation:

Simplifying
p(p + 18) = -77

Reorder the terms:
p(18 + p) = -77
(18 * p + p * p) = -77
(18p + p2) = -77

Solving
18p + p2 = -77

Solving for variable 'p'.

Reorder the terms:
77 + 18p + p2 = -77 + 77

Combine like terms: -77 + 77 = 0
77 + 18p + p2 = 0

Factor a trinomial.
(11 + p)(7 + p) = 0

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 '(7 + p)' equal to zero and attempt to solve:

Simplifying
7 + p = 0

Solving
7 + p = 0

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

Add '-7' to each side of the equation.
7 + -7 + p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + p = 0 + -7
p = 0 + -7

Combine like terms: 0 + -7 = -7
p = -7

Simplifying
p = -7
Solution
p = {-11, -7}