lg^2x-lgx=0

Solution for lg^2x-lgx=0 equation:

Simplifying
lg2x + -1lgx = 0

Reorder the terms:
-1glx + g2lx = 0

Solving
-1glx + g2lx = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), 'glx'.
glx(-1 + g) = 0

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

Simplifying
glx = 0

Solving
glx = 0

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

Simplifying
glx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + g)' equal to zero and attempt to solve:

Simplifying
-1 + g = 0

Solving
-1 + g = 0

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

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

Combine like terms: -1 + 1 = 0
0 + g = 0 + 1
g = 0 + 1

Combine like terms: 0 + 1 = 1
g = 1

Simplifying
g = 1
Solution
g = {1}