n(2n^3+n^2)=6n^2

Solution for n(2n^3+n^2)=6n^2 equation:

Simplifying
n(2n3 + n2) = 6n2

Reorder the terms:
n(n2 + 2n3) = 6n2
(n2 * n + 2n3 * n) = 6n2
(n3 + 2n4) = 6n2

Solving
n3 + 2n4 = 6n2

Solving for variable 'n'.

Reorder the terms:
-6n2 + n3 + 2n4 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-6n2 + n3 + 2n4 = 0

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

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

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 '(-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 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {0, -2, 1.5}