18750=-2p^2+400p

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Solution for 18750=-2p^2+400p equation:


Simplifying
18750 = -2p2 + 400p

Reorder the terms:
18750 = 400p + -2p2

Solving
18750 = 400p + -2p2

Solving for variable 'p'.

Reorder the terms:
18750 + -400p + 2p2 = 400p + -400p + -2p2 + 2p2

Combine like terms: 400p + -400p = 0
18750 + -400p + 2p2 = 0 + -2p2 + 2p2
18750 + -400p + 2p2 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
18750 + -400p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9375 + -200p + p2) = 0

Factor a trinomial.
2((75 + -1p)(125 + -1p)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(75 + -1p)' equal to zero and attempt to solve: Simplifying 75 + -1p = 0 Solving 75 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + -1p = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -1p = 0 + -75 -1p = 0 + -75 Combine like terms: 0 + -75 = -75 -1p = -75 Divide each side by '-1'. p = 75 Simplifying p = 75

Subproblem 2

Set the factor '(125 + -1p)' equal to zero and attempt to solve: Simplifying 125 + -1p = 0 Solving 125 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + -1p = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -1p = 0 + -125 -1p = 0 + -125 Combine like terms: 0 + -125 = -125 -1p = -125 Divide each side by '-1'. p = 125 Simplifying p = 125

Solution

p = {75, 125}

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