(2y+3)(4-y)=0

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Solution for (2y+3)(4-y)=0 equation:


Simplifying
(2y + 3)(4 + -1y) = 0

Reorder the terms:
(3 + 2y)(4 + -1y) = 0

Multiply (3 + 2y) * (4 + -1y)
(3(4 + -1y) + 2y * (4 + -1y)) = 0
((4 * 3 + -1y * 3) + 2y * (4 + -1y)) = 0
((12 + -3y) + 2y * (4 + -1y)) = 0
(12 + -3y + (4 * 2y + -1y * 2y)) = 0
(12 + -3y + (8y + -2y2)) = 0

Combine like terms: -3y + 8y = 5y
(12 + 5y + -2y2) = 0

Solving
12 + 5y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y)(3 + 2y) = 0

Subproblem 1

Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4

Subproblem 2

Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5

Solution

y = {4, -1.5}

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