(2y+3)(y-9)=0

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Solution for (2y+3)(y-9)=0 equation:


Simplifying
(2y + 3)(y + -9) = 0

Reorder the terms:
(3 + 2y)(y + -9) = 0

Reorder the terms:
(3 + 2y)(-9 + y) = 0

Multiply (3 + 2y) * (-9 + y)
(3(-9 + y) + 2y * (-9 + y)) = 0
((-9 * 3 + y * 3) + 2y * (-9 + y)) = 0
((-27 + 3y) + 2y * (-9 + y)) = 0
(-27 + 3y + (-9 * 2y + y * 2y)) = 0
(-27 + 3y + (-18y + 2y2)) = 0

Combine like terms: 3y + -18y = -15y
(-27 + -15y + 2y2) = 0

Solving
-27 + -15y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y)(9 + -1y) = 0

Subproblem 1

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

Subproblem 2

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

Solution

y = {-1.5, 9}

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