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Simplifying y3 + 6y2 + 12y + 8y = 0 Reorder the terms: 12y + 8y + 6y2 + y3 = 0 Combine like terms: 12y + 8y = 20y 20y + 6y2 + y3 = 0 Solving 20y + 6y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(20 + 6y + y2) = 0Subproblem 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 '(20 + 6y + y2)' equal to zero and attempt to solve: Simplifying 20 + 6y + y2 = 0 Solving 20 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 6y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + 6y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 6y + y2 = 0 + -20 6y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 6y + y2 = -20 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -20 + 9 Reorder the terms: 9 + 6y + y2 = -20 + 9 Combine like terms: -20 + 9 = -11 9 + 6y + y2 = -11 Factor a perfect square on the left side: (y + 3)(y + 3) = -11 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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