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

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


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

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

Multiply (-5 + 2y) * (9 + -1y)
(-5(9 + -1y) + 2y * (9 + -1y)) = 0
((9 * -5 + -1y * -5) + 2y * (9 + -1y)) = 0
((-45 + 5y) + 2y * (9 + -1y)) = 0
(-45 + 5y + (9 * 2y + -1y * 2y)) = 0
(-45 + 5y + (18y + -2y2)) = 0

Combine like terms: 5y + 18y = 23y
(-45 + 23y + -2y2) = 0

Solving
-45 + 23y + -2y2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(-9 + y)' equal to zero and attempt to solve:

Simplifying
-9 + y = 0

Solving
-9 + y = 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 + y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + y = 0 + 9
y = 0 + 9

Combine like terms: 0 + 9 = 9
y = 9

Simplifying
y = 9

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {9, 2.5}

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