30n^4-21n^3-18n^2=0

Solution for 30n^4-21n^3-18n^2=0 equation:

Simplifying
30n4 + -21n3 + -18n2 = 0

Reorder the terms:
-18n2 + -21n3 + 30n4 = 0

Solving
-18n2 + -21n3 + 30n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n2'.
3n2(-6 + -7n + 10n2) = 0

Factor a trinomial.
3n2((-1 + -2n)(6 + -5n)) = 0

Ignore the factor 3.
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
Subproblem 3
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 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 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {0, -0.5, 1.2}