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Simplifying 3y(y2 + -2y + 4) = 0 Reorder the terms: 3y(4 + -2y + y2) = 0 (4 * 3y + -2y * 3y + y2 * 3y) = 0 (12y + -6y2 + 3y3) = 0 Solving 12y + -6y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(4 + -2y + y2) = 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 '(4 + -2y + y2)' equal to zero and attempt to solve: Simplifying 4 + -2y + y2 = 0 Solving 4 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -2y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -2y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2y + y2 = 0 + -4 -2y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -2y + y2 = -4 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = -4 + 1 Reorder the terms: 1 + -2y + y2 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + -2y + y2 = -3 Factor a perfect square on the left side: (y + -1)(y + -1) = -3 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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