(3+y)(4y-9)=0

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Solution for (3+y)(4y-9)=0 equation:


Simplifying
(3 + y)(4y + -9) = 0

Reorder the terms:
(3 + y)(-9 + 4y) = 0

Multiply (3 + y) * (-9 + 4y)
(3(-9 + 4y) + y(-9 + 4y)) = 0
((-9 * 3 + 4y * 3) + y(-9 + 4y)) = 0
((-27 + 12y) + y(-9 + 4y)) = 0
(-27 + 12y + (-9 * y + 4y * y)) = 0
(-27 + 12y + (-9y + 4y2)) = 0

Combine like terms: 12y + -9y = 3y
(-27 + 3y + 4y2) = 0

Solving
-27 + 3y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(9 + -4y) = 0

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3

Subproblem 2

Set the factor '(9 + -4y)' equal to zero and attempt to solve: Simplifying 9 + -4y = 0 Solving 9 + -4y = 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 + -4y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4y = 0 + -9 -4y = 0 + -9 Combine like terms: 0 + -9 = -9 -4y = -9 Divide each side by '-4'. y = 2.25 Simplifying y = 2.25

Solution

y = {-3, 2.25}

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