0=-48+20p-2p^2

Solution for 0=-48+20p-2p^2 equation:

Simplifying
0 = -48 + 20p + -2p2

Solving
0 = -48 + 20p + -2p2

Solving for variable 'p'.

Combine like terms: 0 + 48 = 48
48 + -20p + 2p2 = -48 + 20p + -2p2 + 48 + -20p + 2p2

Reorder the terms:
48 + -20p + 2p2 = -48 + 48 + 20p + -20p + -2p2 + 2p2

Combine like terms: -48 + 48 = 0
48 + -20p + 2p2 = 0 + 20p + -20p + -2p2 + 2p2
48 + -20p + 2p2 = 20p + -20p + -2p2 + 2p2

Combine like terms: 20p + -20p = 0
48 + -20p + 2p2 = 0 + -2p2 + 2p2
48 + -20p + 2p2 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
48 + -20p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -10p + p2) = 0

Factor a trinomial.
2((4 + -1p)(6 + -1p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
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 = {4, 6}