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Simplifying 2y(y + -1)(y + -3) = 0 Reorder the terms: 2y(-1 + y)(y + -3) = 0 Reorder the terms: 2y(-1 + y)(-3 + y) = 0 Multiply (-1 + y) * (-3 + y) 2y(-1(-3 + y) + y(-3 + y)) = 0 2y((-3 * -1 + y * -1) + y(-3 + y)) = 0 2y((3 + -1y) + y(-3 + y)) = 0 2y(3 + -1y + (-3 * y + y * y)) = 0 2y(3 + -1y + (-3y + y2)) = 0 Combine like terms: -1y + -3y = -4y 2y(3 + -4y + y2) = 0 (3 * 2y + -4y * 2y + y2 * 2y) = 0 (6y + -8y2 + 2y3) = 0 Solving 6y + -8y2 + 2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(3 + -4y + y2) = 0 Factor a trinomial. 2y((1 + -1y)(3 + -1y)) = 0 Ignore the factor 2.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 '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Subproblem 3
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 = 3Solution
y = {0, 1, 3}
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