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Simplifying 2y(3y + -1)(4y + 5) = 0 Reorder the terms: 2y(-1 + 3y)(4y + 5) = 0 Reorder the terms: 2y(-1 + 3y)(5 + 4y) = 0 Multiply (-1 + 3y) * (5 + 4y) 2y(-1(5 + 4y) + 3y * (5 + 4y)) = 0 2y((5 * -1 + 4y * -1) + 3y * (5 + 4y)) = 0 2y((-5 + -4y) + 3y * (5 + 4y)) = 0 2y(-5 + -4y + (5 * 3y + 4y * 3y)) = 0 2y(-5 + -4y + (15y + 12y2)) = 0 Combine like terms: -4y + 15y = 11y 2y(-5 + 11y + 12y2) = 0 (-5 * 2y + 11y * 2y + 12y2 * 2y) = 0 (-10y + 22y2 + 24y3) = 0 Solving -10y + 22y2 + 24y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-5 + 11y + 12y2) = 0 Factor a trinomial. 2y((-5 + -4y)(1 + -3y)) = 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 '(-5 + -4y)' equal to zero and attempt to solve: Simplifying -5 + -4y = 0 Solving -5 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4y = 0 + 5 -4y = 0 + 5 Combine like terms: 0 + 5 = 5 -4y = 5 Divide each side by '-4'. y = -1.25 Simplifying y = -1.25Subproblem 3
Set the factor '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 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 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {0, -1.25, 0.3333333333}
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