X^2(x^2-81)(x^2-1)=0

Solution for X^2(x^2-81)(x^2-1)=0 equation:

Simplifying
X2(x2 + -81)(x2 + -1) = 0

Reorder the terms:
X2(-81 + x2)(x2 + -1) = 0

Reorder the terms:
X2(-81 + x2)(-1 + x2) = 0

Multiply (-81 + x2) * (-1 + x2)
X2(-81(-1 + x2) + x2(-1 + x2)) = 0
X2((-1 * -81 + x2 * -81) + x2(-1 + x2)) = 0
X2((81 + -81x2) + x2(-1 + x2)) = 0
X2(81 + -81x2 + (-1 * x2 + x2 * x2)) = 0
X2(81 + -81x2 + (-1x2 + x4)) = 0

Combine like terms: -81x2 + -1x2 = -82x2
X2(81 + -82x2 + x4) = 0
(81 * X2 + -82x2 * X2 + x4 * X2) = 0
(81X2 + -82x2X2 + x4X2) = 0

Solving
81X2 + -82x2X2 + x4X2 = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X2'.
X2(81 + -82x2 + x4) = 0

Factor a trinomial.
X2((1 + -1x2)(81 + -1x2)) = 0

Factor a difference between two squares.
X2(((1 + x)(1 + -1x))(81 + -1x2)) = 0

Factor a difference between two squares.
X2(((9 + x)(9 + -1x))(1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve:

Simplifying
X2 = 0

Solving
X2 = 0

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

Simplifying
X2 = 0

Take the square root of each side:
X = {0}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Add '-1x' to each side of the equation.
x + -1x = -1 + -1x

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

Simplifying
0 = -1 + -1x

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Add 'x' to each side of the equation.
-1x + x = -1 + x

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

Simplifying
0 = -1 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 4
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Add '-1x' to each side of the equation.
x + -1x = -9 + -1x

Combine like terms: x + -1x = 0
0 = -9 + -1x

Simplifying
0 = -9 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 5
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Add 'x' to each side of the equation.
-1x + x = -9 + x

Combine like terms: -1x + x = 0
0 = -9 + x

Simplifying
0 = -9 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}