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Simplifying 0 = 12y3 + 10y2 + -12y Reorder the terms: 0 = -12y + 10y2 + 12y3 Solving 0 = -12y + 10y2 + 12y3 Solving for variable 'y'. Remove the zero: 12y + -10y2 + -12y3 = -12y + 10y2 + 12y3 + 12y + -10y2 + -12y3 Reorder the terms: 12y + -10y2 + -12y3 = -12y + 12y + 10y2 + -10y2 + 12y3 + -12y3 Combine like terms: -12y + 12y = 0 12y + -10y2 + -12y3 = 0 + 10y2 + -10y2 + 12y3 + -12y3 12y + -10y2 + -12y3 = 10y2 + -10y2 + 12y3 + -12y3 Combine like terms: 10y2 + -10y2 = 0 12y + -10y2 + -12y3 = 0 + 12y3 + -12y3 12y + -10y2 + -12y3 = 12y3 + -12y3 Combine like terms: 12y3 + -12y3 = 0 12y + -10y2 + -12y3 = 0 Factor out the Greatest Common Factor (GCF), '2y'. 2y(6 + -5y + -6y2) = 0 Factor a trinomial. 2y((2 + -3y)(3 + 2y)) = 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 '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Subproblem 3
Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Solution
y = {0, 0.6666666667, -1.5}
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