27y^3-9y^2-6y=0

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Solution for 27y^3-9y^2-6y=0 equation:


Simplifying
27y3 + -9y2 + -6y = 0

Reorder the terms:
-6y + -9y2 + 27y3 = 0

Solving
-6y + -9y2 + 27y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-2 + -3y + 9y2) = 0

Factor a trinomial.
3y((-1 + -3y)(2 + -3y)) = 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 = 0

Subproblem 2

Set the factor '(-1 + -3y)' equal to zero and attempt to solve: Simplifying -1 + -3y = 0 Solving -1 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3y = 0 + 1 -3y = 0 + 1 Combine like terms: 0 + 1 = 1 -3y = 1 Divide each side by '-3'. y = -0.3333333333 Simplifying y = -0.3333333333

Subproblem 3

Set the factor '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667

Solution

y = {0, -0.3333333333, 0.6666666667}

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