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Simplifying 6y(10y2 + -3y + 4) + -3y(4y2 + 7) = 0 Reorder the terms: 6y(4 + -3y + 10y2) + -3y(4y2 + 7) = 0 (4 * 6y + -3y * 6y + 10y2 * 6y) + -3y(4y2 + 7) = 0 (24y + -18y2 + 60y3) + -3y(4y2 + 7) = 0 Reorder the terms: 24y + -18y2 + 60y3 + -3y(7 + 4y2) = 0 24y + -18y2 + 60y3 + (7 * -3y + 4y2 * -3y) = 0 24y + -18y2 + 60y3 + (-21y + -12y3) = 0 Reorder the terms: 24y + -21y + -18y2 + 60y3 + -12y3 = 0 Combine like terms: 24y + -21y = 3y 3y + -18y2 + 60y3 + -12y3 = 0 Combine like terms: 60y3 + -12y3 = 48y3 3y + -18y2 + 48y3 = 0 Solving 3y + -18y2 + 48y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(1 + -6y + 16y2) = 0 Ignore the factor 3.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 + -6y + 16y2)' equal to zero and attempt to solve: Simplifying 1 + -6y + 16y2 = 0 Solving 1 + -6y + 16y2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -0.375y + y2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.375y + -0.0625 + y2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.375y + y2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.375y + y2 = 0 + -0.0625 -0.375y + y2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.375y + y2 = -0.0625 The y term is -0.375y. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375y + 0.03515625 + y2 = -0.0625 + 0.03515625 Reorder the terms: 0.03515625 + -0.375y + y2 = -0.0625 + 0.03515625 Combine like terms: -0.0625 + 0.03515625 = -0.02734375 0.03515625 + -0.375y + y2 = -0.02734375 Factor a perfect square on the left side: (y + -0.1875)(y + -0.1875) = -0.02734375 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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