3n^3-84n=4n^2

Solution for 3n^3-84n=4n^2 equation:

Simplifying
3n3 + -84n = 4n2

Reorder the terms:
-84n + 3n3 = 4n2

Solving
-84n + 3n3 = 4n2

Solving for variable 'n'.

Reorder the terms:
-84n + -4n2 + 3n3 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-84n + -4n2 + 3n3 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-84 + -4n + 3n2) = 0

Factor a trinomial.
n((-14 + -3n)(6 + -1n)) = 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 '(-14 + -3n)' equal to zero and attempt to solve:

Simplifying
-14 + -3n = 0

Solving
-14 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '14' to each side of the equation.
-14 + 14 + -3n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3n = 0 + 14
-3n = 0 + 14

Combine like terms: 0 + 14 = 14
-3n = 14

Divide each side by '-3'.
n = -4.666666667

Simplifying
n = -4.666666667
Subproblem 3
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {0, -4.666666667, 6}