(3y-5)(9+y)=0

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Solution for (3y-5)(9+y)=0 equation:


Simplifying
(3y + -5)(9 + y) = 0

Reorder the terms:
(-5 + 3y)(9 + y) = 0

Multiply (-5 + 3y) * (9 + y)
(-5(9 + y) + 3y * (9 + y)) = 0
((9 * -5 + y * -5) + 3y * (9 + y)) = 0
((-45 + -5y) + 3y * (9 + y)) = 0
(-45 + -5y + (9 * 3y + y * 3y)) = 0
(-45 + -5y + (27y + 3y2)) = 0

Combine like terms: -5y + 27y = 22y
(-45 + 22y + 3y2) = 0

Solving
-45 + 22y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -1y)(5 + -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 '(5 + -3y)' equal to zero and attempt to solve: Simplifying 5 + -3y = 0 Solving 5 + -3y = 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 + -3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3y = 0 + -5 -3y = 0 + -5 Combine like terms: 0 + -5 = -5 -3y = -5 Divide each side by '-3'. y = 1.666666667 Simplifying y = 1.666666667

Solution

y = {-9, 1.666666667}

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