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Simplifying -1y(y2 + -5) + 4y2(7y + -4) = 0 Reorder the terms: -1y(-5 + y2) + 4y2(7y + -4) = 0 (-5 * -1y + y2 * -1y) + 4y2(7y + -4) = 0 (5y + -1y3) + 4y2(7y + -4) = 0 Reorder the terms: 5y + -1y3 + 4y2(-4 + 7y) = 0 5y + -1y3 + (-4 * 4y2 + 7y * 4y2) = 0 5y + -1y3 + (-16y2 + 28y3) = 0 Reorder the terms: 5y + -16y2 + -1y3 + 28y3 = 0 Combine like terms: -1y3 + 28y3 = 27y3 5y + -16y2 + 27y3 = 0 Solving 5y + -16y2 + 27y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(5 + -16y + 27y2) = 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 '(5 + -16y + 27y2)' equal to zero and attempt to solve: Simplifying 5 + -16y + 27y2 = 0 Solving 5 + -16y + 27y2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.1851851852 + -0.5925925926y + y2 = 0 Move the constant term to the right: Add '-0.1851851852' to each side of the equation. 0.1851851852 + -0.5925925926y + -0.1851851852 + y2 = 0 + -0.1851851852 Reorder the terms: 0.1851851852 + -0.1851851852 + -0.5925925926y + y2 = 0 + -0.1851851852 Combine like terms: 0.1851851852 + -0.1851851852 = 0.0000000000 0.0000000000 + -0.5925925926y + y2 = 0 + -0.1851851852 -0.5925925926y + y2 = 0 + -0.1851851852 Combine like terms: 0 + -0.1851851852 = -0.1851851852 -0.5925925926y + y2 = -0.1851851852 The y term is -0.5925925926y. Take half its coefficient (-0.2962962963). Square it (0.08779149520) and add it to both sides. Add '0.08779149520' to each side of the equation. -0.5925925926y + 0.08779149520 + y2 = -0.1851851852 + 0.08779149520 Reorder the terms: 0.08779149520 + -0.5925925926y + y2 = -0.1851851852 + 0.08779149520 Combine like terms: -0.1851851852 + 0.08779149520 = -0.09739369 0.08779149520 + -0.5925925926y + y2 = -0.09739369 Factor a perfect square on the left side: (y + -0.2962962963)(y + -0.2962962963) = -0.09739369 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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