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Simplifying y(y + 3)(y + 2) + -4y(y + 2) = 0 Reorder the terms: y(3 + y)(y + 2) + -4y(y + 2) = 0 Reorder the terms: y(3 + y)(2 + y) + -4y(y + 2) = 0 Multiply (3 + y) * (2 + y) y(3(2 + y) + y(2 + y)) + -4y(y + 2) = 0 y((2 * 3 + y * 3) + y(2 + y)) + -4y(y + 2) = 0 y((6 + 3y) + y(2 + y)) + -4y(y + 2) = 0 y(6 + 3y + (2 * y + y * y)) + -4y(y + 2) = 0 y(6 + 3y + (2y + y2)) + -4y(y + 2) = 0 Combine like terms: 3y + 2y = 5y y(6 + 5y + y2) + -4y(y + 2) = 0 (6 * y + 5y * y + y2 * y) + -4y(y + 2) = 0 (6y + 5y2 + y3) + -4y(y + 2) = 0 Reorder the terms: 6y + 5y2 + y3 + -4y(2 + y) = 0 6y + 5y2 + y3 + (2 * -4y + y * -4y) = 0 6y + 5y2 + y3 + (-8y + -4y2) = 0 Reorder the terms: 6y + -8y + 5y2 + -4y2 + y3 = 0 Combine like terms: 6y + -8y = -2y -2y + 5y2 + -4y2 + y3 = 0 Combine like terms: 5y2 + -4y2 = 1y2 -2y + 1y2 + y3 = 0 Solving -2y + 1y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + y + y2) = 0 Factor a trinomial. y((-2 + -1y)(1 + -1y)) = 0Subproblem 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 '(-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 = -2Subproblem 3
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 = 1Solution
y = {0, -2, 1}
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