3n^4-33n^2+30=

Solution for 3n^4-33n^2+30= equation:

Simplifying
3n4 + -33n2 + 30 = 0

Reorder the terms:
30 + -33n2 + 3n4 = 0

Solving
30 + -33n2 + 3n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -11n2 + n4) = 0

Factor a trinomial.
3((1 + -1n2)(10 + -1n2)) = 0

Factor a difference between two squares.
3(((1 + n)(1 + -1n))(10 + -1n2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(10 + -1n2)' equal to zero and attempt to solve:

Simplifying
10 + -1n2 = 0

Solving
10 + -1n2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n2 = 0 + -10
-1n2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1n2 = -10

Divide each side by '-1'.
n2 = 10

Simplifying
n2 = 10

Take the square root of each side:
n = {-3.16227766, 3.16227766}
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-3.16227766, 3.16227766, -1, 1}