(3-x)(2+x)(1+x)=6

Solution for (3-x)(2+x)(1+x)=6 equation:

Simplifying
(3 + -1x)(2 + x)(1 + x) = 6

Multiply (3 + -1x) * (2 + x)
(3(2 + x) + -1x * (2 + x))(1 + x) = 6
((2 * 3 + x * 3) + -1x * (2 + x))(1 + x) = 6
((6 + 3x) + -1x * (2 + x))(1 + x) = 6
(6 + 3x + (2 * -1x + x * -1x))(1 + x) = 6
(6 + 3x + (-2x + -1x2))(1 + x) = 6

Combine like terms: 3x + -2x = 1x
(6 + 1x + -1x2)(1 + x) = 6

Multiply (6 + 1x + -1x2) * (1 + x)
(6(1 + x) + 1x * (1 + x) + -1x2 * (1 + x)) = 6
((1 * 6 + x * 6) + 1x * (1 + x) + -1x2 * (1 + x)) = 6
((6 + 6x) + 1x * (1 + x) + -1x2 * (1 + x)) = 6
(6 + 6x + (1 * 1x + x * 1x) + -1x2 * (1 + x)) = 6
(6 + 6x + (1x + 1x2) + -1x2 * (1 + x)) = 6
(6 + 6x + 1x + 1x2 + (1 * -1x2 + x * -1x2)) = 6
(6 + 6x + 1x + 1x2 + (-1x2 + -1x3)) = 6

Combine like terms: 6x + 1x = 7x
(6 + 7x + 1x2 + -1x2 + -1x3) = 6

Combine like terms: 1x2 + -1x2 = 0
(6 + 7x + 0 + -1x3) = 6
(6 + 7x + -1x3) = 6

Add '-6' to each side of the equation.
6 + 7x + -6 + -1x3 = 6 + -6

Reorder the terms:
6 + -6 + 7x + -1x3 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + 7x + -1x3 = 6 + -6
7x + -1x3 = 6 + -6

Combine like terms: 6 + -6 = 0
7x + -1x3 = 0

Solving
7x + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -1x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {0, -2.645751311, 2.645751311}