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Simplifying 3y(y + -2)(y + 4) = 3y3 Reorder the terms: 3y(-2 + y)(y + 4) = 3y3 Reorder the terms: 3y(-2 + y)(4 + y) = 3y3 Multiply (-2 + y) * (4 + y) 3y(-2(4 + y) + y(4 + y)) = 3y3 3y((4 * -2 + y * -2) + y(4 + y)) = 3y3 3y((-8 + -2y) + y(4 + y)) = 3y3 3y(-8 + -2y + (4 * y + y * y)) = 3y3 3y(-8 + -2y + (4y + y2)) = 3y3 Combine like terms: -2y + 4y = 2y 3y(-8 + 2y + y2) = 3y3 (-8 * 3y + 2y * 3y + y2 * 3y) = 3y3 (-24y + 6y2 + 3y3) = 3y3 Add '-3y3' to each side of the equation. -24y + 6y2 + 3y3 + -3y3 = 3y3 + -3y3 Combine like terms: 3y3 + -3y3 = 0 -24y + 6y2 + 0 = 3y3 + -3y3 -24y + 6y2 = 3y3 + -3y3 Combine like terms: 3y3 + -3y3 = 0 -24y + 6y2 = 0 Solving -24y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6y'. 6y(-4 + y) = 0 Ignore the factor 6.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 '(-4 + y)' equal to zero and attempt to solve: Simplifying -4 + y = 0 Solving -4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + y = 0 + 4 y = 0 + 4 Combine like terms: 0 + 4 = 4 y = 4 Simplifying y = 4Solution
y = {0, 4}
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