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Simplifying 4y3 = 5y2 + -6y Reorder the terms: 4y3 = -6y + 5y2 Solving 4y3 = -6y + 5y2 Solving for variable 'y'. Reorder the terms: 6y + -5y2 + 4y3 = -6y + 5y2 + 6y + -5y2 Reorder the terms: 6y + -5y2 + 4y3 = -6y + 6y + 5y2 + -5y2 Combine like terms: -6y + 6y = 0 6y + -5y2 + 4y3 = 0 + 5y2 + -5y2 6y + -5y2 + 4y3 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 6y + -5y2 + 4y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(6 + -5y + 4y2) = 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 '(6 + -5y + 4y2)' equal to zero and attempt to solve: Simplifying 6 + -5y + 4y2 = 0 Solving 6 + -5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -1.25y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.25y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.25y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.25y + y2 = 0 + -1.5 -1.25y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.25y + y2 = -1.5 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = -1.5 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = -1.5 + 0.390625 Combine like terms: -1.5 + 0.390625 = -1.109375 0.390625 + -1.25y + y2 = -1.109375 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = -1.109375 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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