12n^7+2n^5=30n^3

Solution for 12n^7+2n^5=30n^3 equation:

Simplifying
12n7 + 2n5 = 30n3

Reorder the terms:
2n5 + 12n7 = 30n3

Solving
2n5 + 12n7 = 30n3

Solving for variable 'n'.

Reorder the terms:
-30n3 + 2n5 + 12n7 = 30n3 + -30n3

Combine like terms: 30n3 + -30n3 = 0
-30n3 + 2n5 + 12n7 = 0

Factor out the Greatest Common Factor (GCF), '2n3'.
2n3(-15 + n2 + 6n4) = 0

Factor a trinomial.
2n3((-5 + -3n2)(3 + -2n2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve:

Simplifying
n3 = 0

Solving
n3 = 0

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

Simplifying
n3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-5 + -3n2)' equal to zero and attempt to solve:

Simplifying
-5 + -3n2 = 0

Solving
-5 + -3n2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3n2 = 0 + 5
-3n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3n2 = 5

Divide each side by '-3'.
n2 = -1.666666667

Simplifying
n2 = -1.666666667

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -2n2)' equal to zero and attempt to solve:

Simplifying
3 + -2n2 = 0

Solving
3 + -2n2 = 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 + -2n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n2 = 0 + -3
-2n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2n2 = -3

Divide each side by '-2'.
n2 = 1.5

Simplifying
n2 = 1.5

Take the square root of each side:
n = {-1.224744871, 1.224744871}
Solution
n = {-1.224744871, 1.224744871}