(x^2-1)(x^2+6)=0

Solution for (x^2-1)(x^2+6)=0 equation:

Simplifying
(x2 + -1)(x2 + 6) = 0

Reorder the terms:
(-1 + x2)(x2 + 6) = 0

Reorder the terms:
(-1 + x2)(6 + x2) = 0

Multiply (-1 + x2) * (6 + x2)
(-1(6 + x2) + x2(6 + x2)) = 0
((6 * -1 + x2 * -1) + x2(6 + x2)) = 0
((-6 + -1x2) + x2(6 + x2)) = 0
(-6 + -1x2 + (6 * x2 + x2 * x2)) = 0
(-6 + -1x2 + (6x2 + x4)) = 0

Combine like terms: -1x2 + 6x2 = 5x2
(-6 + 5x2 + x4) = 0

Solving
-6 + 5x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x2)(1 + -1x2) = 0

Factor a difference between two squares.
(-6 + -1x2)((1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor '(-6 + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x2 = 0

Solving
-6 + -1x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x2 = 0 + 6
-1x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1x2 = 6

Divide each side by '-1'.
x2 = -6

Simplifying
x2 = -6

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 '(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

Simplifying
x = -1
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

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

Simplifying
x = 1
Solution
x = {-1, 1}