(2y-9)(5-y)=0

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Solution for (2y-9)(5-y)=0 equation:


Simplifying
(2y + -9)(5 + -1y) = 0

Reorder the terms:
(-9 + 2y)(5 + -1y) = 0

Multiply (-9 + 2y) * (5 + -1y)
(-9(5 + -1y) + 2y * (5 + -1y)) = 0
((5 * -9 + -1y * -9) + 2y * (5 + -1y)) = 0
((-45 + 9y) + 2y * (5 + -1y)) = 0
(-45 + 9y + (5 * 2y + -1y * 2y)) = 0
(-45 + 9y + (10y + -2y2)) = 0

Combine like terms: 9y + 10y = 19y
(-45 + 19y + -2y2) = 0

Solving
-45 + 19y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + y)(9 + -2y) = 0

Subproblem 1

Set the factor '(-5 + y)' equal to zero and attempt to solve: Simplifying -5 + y = 0 Solving -5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + y = 0 + 5 y = 0 + 5 Combine like terms: 0 + 5 = 5 y = 5 Simplifying y = 5

Subproblem 2

Set the factor '(9 + -2y)' equal to zero and attempt to solve: Simplifying 9 + -2y = 0 Solving 9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2y = 0 + -9 -2y = 0 + -9 Combine like terms: 0 + -9 = -9 -2y = -9 Divide each side by '-2'. y = 4.5 Simplifying y = 4.5

Solution

y = {5, 4.5}

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