4(x^4-81)=0

Solution for 4(x^4-81)=0 equation:

Simplifying
4(x4 + -81) = 0

Reorder the terms:
4(-81 + x4) = 0
(-81 * 4 + x4 * 4) = 0
(-324 + 4x4) = 0

Solving
-324 + 4x4 = 0

Solving for variable 'x'.

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

Add '324' to each side of the equation.
-324 + 324 + 4x4 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + 4x4 = 0 + 324
4x4 = 0 + 324

Combine like terms: 0 + 324 = 324
4x4 = 324

Divide each side by '4'.
x4 = 81

Simplifying
x4 = 81

Reorder the terms:
-81 + x4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + x4 = 0

Factor a difference between two squares.
(9 + x2)(-9 + x2) = 0

Factor a difference between two squares.
(9 + x2)((3 + x)(-3 + x)) = 0

Subproblem 1
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}