4n^3+7n^2-6n=2n^2

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Solution for 4n^3+7n^2-6n=2n^2 equation:


Simplifying
4n3 + 7n2 + -6n = 2n2

Reorder the terms:
-6n + 7n2 + 4n3 = 2n2

Solving
-6n + 7n2 + 4n3 = 2n2

Solving for variable 'n'.

Reorder the terms:
-6n + 7n2 + -2n2 + 4n3 = 2n2 + -2n2

Combine like terms: 7n2 + -2n2 = 5n2
-6n + 5n2 + 4n3 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-6n + 5n2 + 4n3 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6 + 5n + 4n2) = 0

Factor a trinomial.
n((-2 + -1n)(3 + -4n)) = 0

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

Subproblem 3

Set the factor '(3 + -4n)' equal to zero and attempt to solve: Simplifying 3 + -4n = 0 Solving 3 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4n = 0 + -3 -4n = 0 + -3 Combine like terms: 0 + -3 = -3 -4n = -3 Divide each side by '-4'. n = 0.75 Simplifying n = 0.75

Solution

n = {0, -2, 0.75}

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