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Simplifying 5y3 + -10y2 + 15y = 0 Reorder the terms: 15y + -10y2 + 5y3 = 0 Solving 15y + -10y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(3 + -2y + y2) = 0 Ignore the factor 5.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 '(3 + -2y + y2)' equal to zero and attempt to solve: Simplifying 3 + -2y + y2 = 0 Solving 3 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -2y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y + y2 = 0 + -3 -2y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2y + y2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2y + y2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2y + y2 = -2 Factor a perfect square on the left side: (y + -1)(y + -1) = -2 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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