3n^4-147=0

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Solution for 3n^4-147=0 equation: 


Simplifying
3n4 + -147 = 0

Reorder the terms:
-147 + 3n4 = 0

Solving
-147 + 3n4 = 0

Solving for variable 'n'.

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

Add '147' to each side of the equation.
-147 + 147 + 3n4 = 0 + 147

Combine like terms: -147 + 147 = 0
0 + 3n4 = 0 + 147
3n4 = 0 + 147

Combine like terms: 0 + 147 = 147
3n4 = 147

Divide each side by '3'.
n4 = 49

Simplifying
n4 = 49

Reorder the terms:
-49 + n4 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + n4 = 0

Factor a difference between two squares.
(7 + n2)(-7 + n2) = 0


Subproblem 1
Set the factor '(7 + n2)' equal to zero and attempt to solve:

Simplifying
7 + n2 = 0

Solving
7 + n2 = 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 + n2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n2 = 0 + -7
n2 = 0 + -7

Combine like terms: 0 + -7 = -7
n2 = -7

Simplifying
n2 = -7

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 '(-7 + n2)' equal to zero and attempt to solve:

Simplifying
-7 + n2 = 0

Solving
-7 + n2 = 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 + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + n2 = 0 + 7
n2 = 0 + 7

Combine like terms: 0 + 7 = 7
n2 = 7

Simplifying
n2 = 7

Take the square root of each side:
n = {-2.645751311, 2.645751311}
Solution
n = {-2.645751311, 2.645751311}

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