21n^3+138n^2-63n=

Solution for 21n^3+138n^2-63n= equation:

Simplifying
21n3 + 138n2 + -63n = 0

Reorder the terms:
-63n + 138n2 + 21n3 = 0

Solving
-63n + 138n2 + 21n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-21 + 46n + 7n2) = 0

Factor a trinomial.
3n((-7 + -1n)(3 + -7n)) = 0

Ignore the factor 3.
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 '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 3
Set the factor '(3 + -7n)' equal to zero and attempt to solve:

Simplifying
3 + -7n = 0

Solving
3 + -7n = 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 + -7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7n = 0 + -3
-7n = 0 + -3

Combine like terms: 0 + -3 = -3
-7n = -3

Divide each side by '-7'.
n = 0.4285714286

Simplifying
n = 0.4285714286
Solution
n = {0, -7, 0.4285714286}