(2y+5)(3-y)=0

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Solution for (2y+5)(3-y)=0 equation:


Simplifying
(2y + 5)(3 + -1y) = 0

Reorder the terms:
(5 + 2y)(3 + -1y) = 0

Multiply (5 + 2y) * (3 + -1y)
(5(3 + -1y) + 2y * (3 + -1y)) = 0
((3 * 5 + -1y * 5) + 2y * (3 + -1y)) = 0
((15 + -5y) + 2y * (3 + -1y)) = 0
(15 + -5y + (3 * 2y + -1y * 2y)) = 0
(15 + -5y + (6y + -2y2)) = 0

Combine like terms: -5y + 6y = 1y
(15 + 1y + -2y2) = 0

Solving
15 + 1y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -1y)(5 + 2y) = 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 '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5

Solution

y = {3, -2.5}

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