2n^3-2n^2+2n=0

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Solution for 2n^3-2n^2+2n=0 equation:


Simplifying
2n3 + -2n2 + 2n = 0

Reorder the terms:
2n + -2n2 + 2n3 = 0

Solving
2n + -2n2 + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(1 + -1n + n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(1 + -1n + n2)' equal to zero and attempt to solve: Simplifying 1 + -1n + n2 = 0 Solving 1 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -1n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n + n2 = 0 + -1 -1n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1n + n2 = -1 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = -1 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1n + n2 = -0.75 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -0.75 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

n = {0}

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