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Simplifying 3y(y + -2)(y + 3) = 0 Reorder the terms: 3y(-2 + y)(y + 3) = 0 Reorder the terms: 3y(-2 + y)(3 + y) = 0 Multiply (-2 + y) * (3 + y) 3y(-2(3 + y) + y(3 + y)) = 0 3y((3 * -2 + y * -2) + y(3 + y)) = 0 3y((-6 + -2y) + y(3 + y)) = 0 3y(-6 + -2y + (3 * y + y * y)) = 0 3y(-6 + -2y + (3y + y2)) = 0 Combine like terms: -2y + 3y = 1y 3y(-6 + 1y + y2) = 0 (-6 * 3y + 1y * 3y + y2 * 3y) = 0 (-18y + 3y2 + 3y3) = 0 Solving -18y + 3y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(-6 + y + y2) = 0 Factor a trinomial. 3y((-3 + -1y)(2 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 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 = -3Subproblem 3
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 = 2Solution
y = {0, -3, 2}
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