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Simplifying 6y3 + -4y2 + 2y = 0 Reorder the terms: 2y + -4y2 + 6y3 = 0 Solving 2y + -4y2 + 6y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + -2y + 3y2) = 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 '(1 + -2y + 3y2)' equal to zero and attempt to solve: Simplifying 1 + -2y + 3y2 = 0 Solving 1 + -2y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.6666666667y + -0.3333333333 + y2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.6666666667y + y2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.6666666667y + y2 = 0 + -0.3333333333 -0.6666666667y + y2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.6666666667y + y2 = -0.3333333333 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = -0.3333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = -0.3333333333 + 0.1111111112 Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221 0.1111111112 + -0.6666666667y + y2 = -0.2222222221 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = -0.2222222221 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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