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Simplifying 5y3 + -23y2 = 4y2 + 18y Reorder the terms: -23y2 + 5y3 = 4y2 + 18y Reorder the terms: -23y2 + 5y3 = 18y + 4y2 Solving -23y2 + 5y3 = 18y + 4y2 Solving for variable 'y'. Reorder the terms: -18y + -23y2 + -4y2 + 5y3 = 18y + 4y2 + -18y + -4y2 Combine like terms: -23y2 + -4y2 = -27y2 -18y + -27y2 + 5y3 = 18y + 4y2 + -18y + -4y2 Reorder the terms: -18y + -27y2 + 5y3 = 18y + -18y + 4y2 + -4y2 Combine like terms: 18y + -18y = 0 -18y + -27y2 + 5y3 = 0 + 4y2 + -4y2 -18y + -27y2 + 5y3 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -18y + -27y2 + 5y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-18 + -27y + 5y2) = 0 Factor a trinomial. y((-3 + -5y)(6 + -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 '(-3 + -5y)' equal to zero and attempt to solve: Simplifying -3 + -5y = 0 Solving -3 + -5y = 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 + -5y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5y = 0 + 3 -5y = 0 + 3 Combine like terms: 0 + 3 = 3 -5y = 3 Divide each side by '-5'. y = -0.6 Simplifying y = -0.6Subproblem 3
Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Solution
y = {0, -0.6, 6}
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