(x-6)(x+6)(x+3)(x-3)=0

Solution for (x-6)(x+6)(x+3)(x-3)=0 equation:

Simplifying
(x + -6)(x + 6)(x + 3)(x + -3) = 0

Reorder the terms:
(-6 + x)(x + 6)(x + 3)(x + -3) = 0

Reorder the terms:
(-6 + x)(6 + x)(x + 3)(x + -3) = 0

Reorder the terms:
(-6 + x)(6 + x)(3 + x)(x + -3) = 0

Reorder the terms:
(-6 + x)(6 + x)(3 + x)(-3 + x) = 0

Multiply (-6 + x) * (6 + x)
(-6(6 + x) + x(6 + x))(3 + x)(-3 + x) = 0
((6 * -6 + x * -6) + x(6 + x))(3 + x)(-3 + x) = 0
((-36 + -6x) + x(6 + x))(3 + x)(-3 + x) = 0
(-36 + -6x + (6 * x + x * x))(3 + x)(-3 + x) = 0
(-36 + -6x + (6x + x2))(3 + x)(-3 + x) = 0

Combine like terms: -6x + 6x = 0
(-36 + 0 + x2)(3 + x)(-3 + x) = 0
(-36 + x2)(3 + x)(-3 + x) = 0

Multiply (-36 + x2) * (3 + x)
(-36(3 + x) + x2(3 + x))(-3 + x) = 0
((3 * -36 + x * -36) + x2(3 + x))(-3 + x) = 0
((-108 + -36x) + x2(3 + x))(-3 + x) = 0
(-108 + -36x + (3 * x2 + x * x2))(-3 + x) = 0
(-108 + -36x + (3x2 + x3))(-3 + x) = 0
(-108 + -36x + 3x2 + x3)(-3 + x) = 0

Multiply (-108 + -36x + 3x2 + x3) * (-3 + x)
(-108(-3 + x) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0
((-3 * -108 + x * -108) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0
((324 + -108x) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0
(324 + -108x + (-3 * -36x + x * -36x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0
(324 + -108x + (108x + -36x2) + 3x2 * (-3 + x) + x3(-3 + x)) = 0
(324 + -108x + 108x + -36x2 + (-3 * 3x2 + x * 3x2) + x3(-3 + x)) = 0
(324 + -108x + 108x + -36x2 + (-9x2 + 3x3) + x3(-3 + x)) = 0
(324 + -108x + 108x + -36x2 + -9x2 + 3x3 + (-3 * x3 + x * x3)) = 0
(324 + -108x + 108x + -36x2 + -9x2 + 3x3 + (-3x3 + x4)) = 0

Combine like terms: -108x + 108x = 0
(324 + 0 + -36x2 + -9x2 + 3x3 + -3x3 + x4) = 0
(324 + -36x2 + -9x2 + 3x3 + -3x3 + x4) = 0

Combine like terms: -36x2 + -9x2 = -45x2
(324 + -45x2 + 3x3 + -3x3 + x4) = 0

Combine like terms: 3x3 + -3x3 = 0
(324 + -45x2 + 0 + x4) = 0
(324 + -45x2 + x4) = 0

Solving
324 + -45x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(36 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(36 + -1x2) = 0

Factor a difference between two squares.
((6 + x)(6 + -1x))(3 + x)(3 + -1x) = 0

Subproblem 1
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 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 4
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

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

Simplifying
x = 6
Solution
x = {-3, 3, -6, 6}