0=-p^2+160p-4800

Solution for 0=-p^2+160p-4800 equation:

Simplifying
0 = -1p2 + 160p + -4800

Reorder the terms:
0 = -4800 + 160p + -1p2

Solving
0 = -4800 + 160p + -1p2

Solving for variable 'p'.

Combine like terms: 0 + 4800 = 4800
4800 + -160p + p2 = -4800 + 160p + -1p2 + 4800 + -160p + p2

Reorder the terms:
4800 + -160p + p2 = -4800 + 4800 + 160p + -160p + -1p2 + p2

Combine like terms: -4800 + 4800 = 0
4800 + -160p + p2 = 0 + 160p + -160p + -1p2 + p2
4800 + -160p + p2 = 160p + -160p + -1p2 + p2

Combine like terms: 160p + -160p = 0
4800 + -160p + p2 = 0 + -1p2 + p2
4800 + -160p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
4800 + -160p + p2 = 0

Factor a trinomial.
(40 + -1p)(120 + -1p) = 0

Subproblem 1
Set the factor '(40 + -1p)' equal to zero and attempt to solve:

Simplifying
40 + -1p = 0

Solving
40 + -1p = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1p = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1p = 0 + -40
-1p = 0 + -40

Combine like terms: 0 + -40 = -40
-1p = -40

Divide each side by '-1'.
p = 40

Simplifying
p = 40
Subproblem 2
Set the factor '(120 + -1p)' equal to zero and attempt to solve:

Simplifying
120 + -1p = 0

Solving
120 + -1p = 0

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

Add '-120' to each side of the equation.
120 + -120 + -1p = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -1p = 0 + -120
-1p = 0 + -120

Combine like terms: 0 + -120 = -120
-1p = -120

Divide each side by '-1'.
p = 120

Simplifying
p = 120
Solution
p = {40, 120}