p^2+24=-11p

Solution for p^2+24=-11p equation:

Simplifying
p2 + 24 = -11p

Reorder the terms:
24 + p2 = -11p

Solving
24 + p2 = -11p

Solving for variable 'p'.

Reorder the terms:
24 + 11p + p2 = -11p + 11p

Combine like terms: -11p + 11p = 0
24 + 11p + p2 = 0

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

Subproblem 1
Set the factor '(8 + p)' equal to zero and attempt to solve:

Simplifying
8 + p = 0

Solving
8 + p = 0

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

Add '-8' to each side of the equation.
8 + -8 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
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 = {-8, -3}