0=4n^3-2n^2

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Solution for 0=4n^3-2n^2 equation:


Simplifying
0 = 4n3 + -2n2

Reorder the terms:
0 = -2n2 + 4n3

Solving
0 = -2n2 + 4n3

Solving for variable 'n'.
Remove the zero:
2n2 + -4n3 = -2n2 + 4n3 + 2n2 + -4n3

Reorder the terms:
2n2 + -4n3 = -2n2 + 2n2 + 4n3 + -4n3

Combine like terms: -2n2 + 2n2 = 0
2n2 + -4n3 = 0 + 4n3 + -4n3
2n2 + -4n3 = 4n3 + -4n3

Combine like terms: 4n3 + -4n3 = 0
2n2 + -4n3 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}

Subproblem 2

Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5

Solution

n = {0, 0.5}

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