((3+x)(3+-1x))(2+x)(2+-1x)=0

Solution for ((3+x)(3+-1x))(2+x)(2+-1x)=0 equation:

Simplifying
((3 + x)(3 + -1x))(2 + x)(2 + -1x) = 0

Multiply (3 + x) * (3 + -1x)
((3(3 + -1x) + x(3 + -1x)))(2 + x)(2 + -1x) = 0
(((3 * 3 + -1x * 3) + x(3 + -1x)))(2 + x)(2 + -1x) = 0
(((9 + -3x) + x(3 + -1x)))(2 + x)(2 + -1x) = 0
((9 + -3x + (3 * x + -1x * x)))(2 + x)(2 + -1x) = 0
((9 + -3x + (3x + -1x2)))(2 + x)(2 + -1x) = 0

Combine like terms: -3x + 3x = 0
((9 + 0 + -1x2))(2 + x)(2 + -1x) = 0
((9 + -1x2))(2 + x)(2 + -1x) = 0

Multiply (9 + -1x2) * (2 + x)
(9(2 + x) + -1x2 * (2 + x))(2 + -1x) = 0
((2 * 9 + x * 9) + -1x2 * (2 + x))(2 + -1x) = 0
((18 + 9x) + -1x2 * (2 + x))(2 + -1x) = 0
(18 + 9x + (2 * -1x2 + x * -1x2))(2 + -1x) = 0
(18 + 9x + (-2x2 + -1x3))(2 + -1x) = 0
(18 + 9x + -2x2 + -1x3)(2 + -1x) = 0

Multiply (18 + 9x + -2x2 + -1x3) * (2 + -1x)
(18(2 + -1x) + 9x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) = 0
((2 * 18 + -1x * 18) + 9x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) = 0
((36 + -18x) + 9x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) = 0
(36 + -18x + (2 * 9x + -1x * 9x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) = 0
(36 + -18x + (18x + -9x2) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) = 0
(36 + -18x + 18x + -9x2 + (2 * -2x2 + -1x * -2x2) + -1x3 * (2 + -1x)) = 0
(36 + -18x + 18x + -9x2 + (-4x2 + 2x3) + -1x3 * (2 + -1x)) = 0
(36 + -18x + 18x + -9x2 + -4x2 + 2x3 + (2 * -1x3 + -1x * -1x3)) = 0
(36 + -18x + 18x + -9x2 + -4x2 + 2x3 + (-2x3 + 1x4)) = 0

Combine like terms: -18x + 18x = 0
(36 + 0 + -9x2 + -4x2 + 2x3 + -2x3 + 1x4) = 0
(36 + -9x2 + -4x2 + 2x3 + -2x3 + 1x4) = 0

Combine like terms: -9x2 + -4x2 = -13x2
(36 + -13x2 + 2x3 + -2x3 + 1x4) = 0

Combine like terms: 2x3 + -2x3 = 0
(36 + -13x2 + 0 + 1x4) = 0
(36 + -13x2 + 1x4) = 0

Solving
36 + -13x2 + 1x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(9 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(2 + x)(2 + -1x) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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
Subproblem 4
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
Solution
x = {-2, 2, -3, 3}