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Simplifying 6y3(2y2 + -4y + 3) = 0 Reorder the terms: 6y3(3 + -4y + 2y2) = 0 (3 * 6y3 + -4y * 6y3 + 2y2 * 6y3) = 0 (18y3 + -24y4 + 12y5) = 0 Solving 18y3 + -24y4 + 12y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6y3'. 6y3(3 + -4y + 2y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + -4y + 2y2)' equal to zero and attempt to solve: Simplifying 3 + -4y + 2y2 = 0 Solving 3 + -4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -2y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2y + y2 = 0 + -1.5 -2y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2y + y2 = -1.5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = -1.5 + 1 Reorder the terms: 1 + -2y + y2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2y + y2 = -0.5 Factor a perfect square on the left side: (y + -1)(y + -1) = -0.5 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. The solution to this equation could not be determined.
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