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

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


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

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

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

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

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

Solving
-6 + -1y + y2 = 0

Solving for variable 'y'.

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

Solution

y = {-2, 3}

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