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Simplifying -30y4 + 8y3 + -72y2 = 0 Reorder the terms: -72y2 + 8y3 + -30y4 = 0 Solving -72y2 + 8y3 + -30y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(-36 + 4y + -15y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-36 + 4y + -15y2)' equal to zero and attempt to solve: Simplifying -36 + 4y + -15y2 = 0 Solving -36 + 4y + -15y2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 2.4 + -0.2666666667y + y2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -0.2666666667y + -2.4 + y2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -0.2666666667y + y2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -0.2666666667y + y2 = 0 + -2.4 -0.2666666667y + y2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -0.2666666667y + y2 = -2.4 The y term is -0.2666666667y. Take half its coefficient (-0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. -0.2666666667y + 0.01777777780 + y2 = -2.4 + 0.01777777780 Reorder the terms: 0.01777777780 + -0.2666666667y + y2 = -2.4 + 0.01777777780 Combine like terms: -2.4 + 0.01777777780 = -2.3822222222 0.01777777780 + -0.2666666667y + y2 = -2.3822222222 Factor a perfect square on the left side: (y + -0.1333333334)(y + -0.1333333334) = -2.3822222222 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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