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

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


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

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

Multiply (2 + -1y) * (3 + 2y)
(2(3 + 2y) + -1y * (3 + 2y)) = 0
((3 * 2 + 2y * 2) + -1y * (3 + 2y)) = 0
((6 + 4y) + -1y * (3 + 2y)) = 0
(6 + 4y + (3 * -1y + 2y * -1y)) = 0
(6 + 4y + (-3y + -2y2)) = 0

Combine like terms: 4y + -3y = 1y
(6 + 1y + -2y2) = 0

Solving
6 + 1y + -2y2 = 0

Solving for variable 'y'.

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

Subproblem 1

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

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 = {2, -1.5}

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