lx-1l+2lx-2l+lx-3l=0

Solution for lx-1l+2lx-2l+lx-3l=0 equation:

Simplifying
lx + -1l + 2lx + -2l + lx + -3l = 0

Reorder the terms:
-1l + -2l + -3l + lx + 2lx + lx = 0

Combine like terms: -1l + -2l = -3l
-3l + -3l + lx + 2lx + lx = 0

Combine like terms: -3l + -3l = -6l
-6l + lx + 2lx + lx = 0

Combine like terms: lx + 2lx = 3lx
-6l + 3lx + lx = 0

Combine like terms: 3lx + lx = 4lx
-6l + 4lx = 0

Solving
-6l + 4lx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '2l'.
2l(-3 + 2x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'l' equal to zero and attempt to solve:

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

Move all terms containing l 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

Add '-2x' to each side of the equation.
2x + -2x = 3 + -2x

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

Simplifying
0 = 3 + -2x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
l = {0}