p^2=-2p+48

Solution for p^2=-2p+48 equation:

Simplifying
p2 = -2p + 48

Reorder the terms:
p2 = 48 + -2p

Solving
p2 = 48 + -2p

Solving for variable 'p'.

Reorder the terms:
-48 + 2p + p2 = 48 + -2p + -48 + 2p

Reorder the terms:
-48 + 2p + p2 = 48 + -48 + -2p + 2p

Combine like terms: 48 + -48 = 0
-48 + 2p + p2 = 0 + -2p + 2p
-48 + 2p + p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
-48 + 2p + p2 = 0

Factor a trinomial.
(-8 + -1p)(6 + -1p) = 0

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

Simplifying
-8 + -1p = 0

Solving
-8 + -1p = 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 + -1p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1p = 0 + 8
-1p = 0 + 8

Combine like terms: 0 + 8 = 8
-1p = 8

Divide each side by '-1'.
p = -8

Simplifying
p = -8
Subproblem 2
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
Solution
p = {-8, 6}