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Simplifying 2y(4y2 + -3y + -6) = 0 Reorder the terms: 2y(-6 + -3y + 4y2) = 0 (-6 * 2y + -3y * 2y + 4y2 * 2y) = 0 (-12y + -6y2 + 8y3) = 0 Solving -12y + -6y2 + 8y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-6 + -3y + 4y2) = 0 Ignore the factor 2.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 '(-6 + -3y + 4y2)' equal to zero and attempt to solve: Simplifying -6 + -3y + 4y2 = 0 Solving -6 + -3y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -0.75y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.75y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.75y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.75y + y2 = 0 + 1.5 -0.75y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.75y + y2 = 1.5 The y term is -0.75y. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75y + 0.140625 + y2 = 1.5 + 0.140625 Reorder the terms: 0.140625 + -0.75y + y2 = 1.5 + 0.140625 Combine like terms: 1.5 + 0.140625 = 1.640625 0.140625 + -0.75y + y2 = 1.640625 Factor a perfect square on the left side: (y + -0.375)(y + -0.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (y + -0.375) equal to 1.280868846 and -1.280868846.Subproblem 1
y + -0.375 = 1.280868846 Simplifying y + -0.375 = 1.280868846 Reorder the terms: -0.375 + y = 1.280868846 Solving -0.375 + y = 1.280868846 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = 1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = 1.280868846 + 0.375 y = 1.280868846 + 0.375 Combine like terms: 1.280868846 + 0.375 = 1.655868846 y = 1.655868846 Simplifying y = 1.655868846Subproblem 2
y + -0.375 = -1.280868846 Simplifying y + -0.375 = -1.280868846 Reorder the terms: -0.375 + y = -1.280868846 Solving -0.375 + y = -1.280868846 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = -1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = -1.280868846 + 0.375 y = -1.280868846 + 0.375 Combine like terms: -1.280868846 + 0.375 = -0.905868846 y = -0.905868846 Simplifying y = -0.905868846Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.655868846, -0.905868846}Solution
y = {0, 1.655868846, -0.905868846}
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