280=y(34-y)

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Solution for 280=y(34-y) equation:


Simplifying
280 = y(34 + -1y)
280 = (34 * y + -1y * y)
280 = (34y + -1y2)

Solving
280 = 34y + -1y2

Solving for variable 'y'.

Reorder the terms:
280 + -34y + y2 = 34y + -34y + -1y2 + y2

Combine like terms: 34y + -34y = 0
280 + -34y + y2 = 0 + -1y2 + y2
280 + -34y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
280 + -34y + y2 = 0

Factor a trinomial.
(14 + -1y)(20 + -1y) = 0

Subproblem 1

Set the factor '(14 + -1y)' equal to zero and attempt to solve: Simplifying 14 + -1y = 0 Solving 14 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1y = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1y = 0 + -14 -1y = 0 + -14 Combine like terms: 0 + -14 = -14 -1y = -14 Divide each side by '-1'. y = 14 Simplifying y = 14

Subproblem 2

Set the factor '(20 + -1y)' equal to zero and attempt to solve: Simplifying 20 + -1y = 0 Solving 20 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1y = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1y = 0 + -20 -1y = 0 + -20 Combine like terms: 0 + -20 = -20 -1y = -20 Divide each side by '-1'. y = 20 Simplifying y = 20

Solution

y = {14, 20}

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