0=2p^2-200p+5000

Solution for 0=2p^2-200p+5000 equation:

Simplifying
0 = 2p2 + -200p + 5000

Reorder the terms:
0 = 5000 + -200p + 2p2

Solving
0 = 5000 + -200p + 2p2

Solving for variable 'p'.

Combine like terms: 0 + -5000 = -5000
-5000 + 200p + -2p2 = 5000 + -200p + 2p2 + -5000 + 200p + -2p2

Reorder the terms:
-5000 + 200p + -2p2 = 5000 + -5000 + -200p + 200p + 2p2 + -2p2

Combine like terms: 5000 + -5000 = 0
-5000 + 200p + -2p2 = 0 + -200p + 200p + 2p2 + -2p2
-5000 + 200p + -2p2 = -200p + 200p + 2p2 + -2p2

Combine like terms: -200p + 200p = 0
-5000 + 200p + -2p2 = 0 + 2p2 + -2p2
-5000 + 200p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-5000 + 200p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2500 + 100p + -1p2) = 0

Factor a trinomial.
2((-50 + p)(50 + -1p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + p)' equal to zero and attempt to solve:

Simplifying
-50 + p = 0

Solving
-50 + p = 0

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

Add '50' to each side of the equation.
-50 + 50 + p = 0 + 50

Combine like terms: -50 + 50 = 0
0 + p = 0 + 50
p = 0 + 50

Combine like terms: 0 + 50 = 50
p = 50

Simplifying
p = 50
Subproblem 2
Set the factor '(50 + -1p)' equal to zero and attempt to solve:

Simplifying
50 + -1p = 0

Solving
50 + -1p = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1p = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1p = 0 + -50
-1p = 0 + -50

Combine like terms: 0 + -50 = -50
-1p = -50

Divide each side by '-1'.
p = 50

Simplifying
p = 50
Solution
p = {50, 50}