p^2=-p+30

Solution for p^2=-p+30 equation:

Simplifying
p2 = -1p + 30

Reorder the terms:
p2 = 30 + -1p

Solving
p2 = 30 + -1p

Solving for variable 'p'.

Reorder the terms:
-30 + p + p2 = 30 + -1p + -30 + p

Reorder the terms:
-30 + p + p2 = 30 + -30 + -1p + p

Combine like terms: 30 + -30 = 0
-30 + p + p2 = 0 + -1p + p
-30 + p + p2 = -1p + p

Combine like terms: -1p + p = 0
-30 + p + p2 = 0

Factor a trinomial.
(-6 + -1p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve:

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1p = 0 + 6
-1p = 0 + 6

Combine like terms: 0 + 6 = 6
-1p = 6

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 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 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {-6, 5}