6*(3+x)*(2-x)=0

Solution for 6*(3+x)*(2-x)=0 equation:

Simplifying
6(3 + x)(2 + -1x) = 0

Multiply (3 + x) * (2 + -1x)
6(3(2 + -1x) + x(2 + -1x)) = 0
6((2 * 3 + -1x * 3) + x(2 + -1x)) = 0
6((6 + -3x) + x(2 + -1x)) = 0
6(6 + -3x + (2 * x + -1x * x)) = 0
6(6 + -3x + (2x + -1x2)) = 0

Combine like terms: -3x + 2x = -1x
6(6 + -1x + -1x2) = 0
(6 * 6 + -1x * 6 + -1x2 * 6) = 0
(36 + -6x + -6x2) = 0

Solving
36 + -6x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -1x + -1x2) = 0

Factor a trinomial.
6((2 + -1x)(3 + x)) = 0

Ignore the factor 6.
Subproblem 1
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 2
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
Solution
x = {2, -3}