p^2+75=-20p

Solution for p^2+75=-20p equation:

Simplifying
p2 + 75 = -20p

Reorder the terms:
75 + p2 = -20p

Solving
75 + p2 = -20p

Solving for variable 'p'.

Reorder the terms:
75 + 20p + p2 = -20p + 20p

Combine like terms: -20p + 20p = 0
75 + 20p + p2 = 0

Factor a trinomial.
(15 + p)(5 + p) = 0

Subproblem 1
Set the factor '(15 + p)' equal to zero and attempt to solve:

Simplifying
15 + p = 0

Solving
15 + p = 0

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

Add '-15' to each side of the equation.
15 + -15 + p = 0 + -15

Combine like terms: 15 + -15 = 0
0 + p = 0 + -15
p = 0 + -15

Combine like terms: 0 + -15 = -15
p = -15

Simplifying
p = -15
Subproblem 2
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 0

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

Add '-5' to each side of the equation.
5 + -5 + p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + p = 0 + -5
p = 0 + -5

Combine like terms: 0 + -5 = -5
p = -5

Simplifying
p = -5
Solution
p = {-15, -5}