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

Solution for 6(-3+-2x)(2+-1x)=0 equation:

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

Multiply (-3 + -2x) * (2 + -1x)
6(-3(2 + -1x) + -2x * (2 + -1x)) = 0
6((2 * -3 + -1x * -3) + -2x * (2 + -1x)) = 0
6((-6 + 3x) + -2x * (2 + -1x)) = 0
6(-6 + 3x + (2 * -2x + -1x * -2x)) = 0
6(-6 + 3x + (-4x + 2x2)) = 0

Combine like terms: 3x + -4x = -1x
6(-6 + -1x + 2x2) = 0
(-6 * 6 + -1x * 6 + 2x2 * 6) = 0
(-36 + -6x + 12x2) = 0

Solving
-36 + -6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -1x + 2x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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
Solution
x = {-1.5, 2}