(2y+9)(8-y)=0

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Solution for (2y+9)(8-y)=0 equation: 


Simplifying
(2y + 9)(8 + -1y) = 0

Reorder the terms:
(9 + 2y)(8 + -1y) = 0

Multiply (9 + 2y) * (8 + -1y)
(9(8 + -1y) + 2y * (8 + -1y)) = 0
((8 * 9 + -1y * 9) + 2y * (8 + -1y)) = 0
((72 + -9y) + 2y * (8 + -1y)) = 0
(72 + -9y + (8 * 2y + -1y * 2y)) = 0
(72 + -9y + (16y + -2y2)) = 0

Combine like terms: -9y + 16y = 7y
(72 + 7y + -2y2) = 0

Solving
72 + 7y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y)(9 + 2y) = 0


Subproblem 1
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

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 = {8, -4.5}

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