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.
(-6 + -1p)(8 + -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 '(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
Solution
p = {-6, 8}