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Simplifying 120y3 + 72y2 = 140y2 + 84y Reorder the terms: 72y2 + 120y3 = 140y2 + 84y Reorder the terms: 72y2 + 120y3 = 84y + 140y2 Solving 72y2 + 120y3 = 84y + 140y2 Solving for variable 'y'. Reorder the terms: -84y + 72y2 + -140y2 + 120y3 = 84y + 140y2 + -84y + -140y2 Combine like terms: 72y2 + -140y2 = -68y2 -84y + -68y2 + 120y3 = 84y + 140y2 + -84y + -140y2 Reorder the terms: -84y + -68y2 + 120y3 = 84y + -84y + 140y2 + -140y2 Combine like terms: 84y + -84y = 0 -84y + -68y2 + 120y3 = 0 + 140y2 + -140y2 -84y + -68y2 + 120y3 = 140y2 + -140y2 Combine like terms: 140y2 + -140y2 = 0 -84y + -68y2 + 120y3 = 0 Factor out the Greatest Common Factor (GCF), '4y'. 4y(-21 + -17y + 30y2) = 0 Factor a trinomial. 4y((-3 + -5y)(7 + -6y)) = 0 Ignore the factor 4.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 '(-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 '(7 + -6y)' equal to zero and attempt to solve: Simplifying 7 + -6y = 0 Solving 7 + -6y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6y = 0 + -7 -6y = 0 + -7 Combine like terms: 0 + -7 = -7 -6y = -7 Divide each side by '-6'. y = 1.166666667 Simplifying y = 1.166666667Solution
y = {0, -0.6, 1.166666667}
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