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Simplifying 3y3 + -12y2 = 5y2 + 6y Reorder the terms: -12y2 + 3y3 = 5y2 + 6y Reorder the terms: -12y2 + 3y3 = 6y + 5y2 Solving -12y2 + 3y3 = 6y + 5y2 Solving for variable 'y'. Reorder the terms: -6y + -12y2 + -5y2 + 3y3 = 6y + 5y2 + -6y + -5y2 Combine like terms: -12y2 + -5y2 = -17y2 -6y + -17y2 + 3y3 = 6y + 5y2 + -6y + -5y2 Reorder the terms: -6y + -17y2 + 3y3 = 6y + -6y + 5y2 + -5y2 Combine like terms: 6y + -6y = 0 -6y + -17y2 + 3y3 = 0 + 5y2 + -5y2 -6y + -17y2 + 3y3 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 -6y + -17y2 + 3y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-6 + -17y + 3y2) = 0 Factor a trinomial. y((-1 + -3y)(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 '(-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 = -0.3333333333Subproblem 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, -0.3333333333, 6}
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