n(2n^2-12ny+18y^2)=

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Solution for n(2n^2-12ny+18y^2)= equation:


Simplifying
n(2n2 + -12ny + 18y2) = 0

Reorder the terms:
n(-12ny + 2n2 + 18y2) = 0
(-12ny * n + 2n2 * n + 18y2 * n) = 0

Reorder the terms:
(18ny2 + -12n2y + 2n3) = 0
(18ny2 + -12n2y + 2n3) = 0

Solving
18ny2 + -12n2y + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(9y2 + -6ny + n2) = 0

Factor a trinomial.
2n((3y + -1n)(3y + -1n)) = 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 '(3y + -1n)' equal to zero and attempt to solve: Simplifying 3y + -1n = 0 Reorder the terms: -1n + 3y = 0 Solving -1n + 3y = 0 Move all terms containing n to the left, all other terms to the right. Add '-3y' to each side of the equation. -1n + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -1n + 0 = 0 + -3y -1n = 0 + -3y Remove the zero: -1n = -3y Divide each side by '-1'. n = 3y Simplifying n = 3y

Subproblem 3

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

Solution

n = {0, 3y, 3y}

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