(3y+8)(9-y)=0

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Solution for (3y+8)(9-y)=0 equation: 


Simplifying
(3y + 8)(9 + -1y) = 0

Reorder the terms:
(8 + 3y)(9 + -1y) = 0

Multiply (8 + 3y) * (9 + -1y)
(8(9 + -1y) + 3y * (9 + -1y)) = 0
((9 * 8 + -1y * 8) + 3y * (9 + -1y)) = 0
((72 + -8y) + 3y * (9 + -1y)) = 0
(72 + -8y + (9 * 3y + -1y * 3y)) = 0
(72 + -8y + (27y + -3y2)) = 0

Combine like terms: -8y + 27y = 19y
(72 + 19y + -3y2) = 0

Solving
72 + 19y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(9 + -1y)(8 + 3y) = 0


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

Simplifying
9 + -1y = 0

Solving
9 + -1y = 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 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9

Subproblem 2
Set the factor '(8 + 3y)' equal to zero and attempt to solve:

Simplifying
8 + 3y = 0

Solving
8 + 3y = 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 + 3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3y = 0 + -8
3y = 0 + -8

Combine like terms: 0 + -8 = -8
3y = -8

Divide each side by '3'.
y = -2.666666667

Simplifying
y = -2.666666667
Solution
y = {9, -2.666666667}

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