lg(x^2-3x)=lg(3x-8)

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Solution for lg(x^2-3x)=lg(3x-8) equation: 


Simplifying
lg(x2 + -3x) = lg(3x + -8)

Reorder the terms:
gl(-3x + x2) = lg(3x + -8)
(-3x * gl + x2 * gl) = lg(3x + -8)
(-3glx + glx2) = lg(3x + -8)

Reorder the terms:
-3glx + glx2 = gl(-8 + 3x)
-3glx + glx2 = (-8 * gl + 3x * gl)
-3glx + glx2 = (-8gl + 3glx)

Solving
-3glx + glx2 = -8gl + 3glx

Solving for variable 'g'.

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

Add '8gl' to each side of the equation.
-3glx + 8gl + glx2 = -8gl + 8gl + 3glx

Reorder the terms:
8gl + -3glx + glx2 = -8gl + 8gl + 3glx

Combine like terms: -8gl + 8gl = 0
8gl + -3glx + glx2 = 0 + 3glx
8gl + -3glx + glx2 = 3glx

Add '-3glx' to each side of the equation.
8gl + -3glx + -3glx + glx2 = 3glx + -3glx

Combine like terms: -3glx + -3glx = -6glx
8gl + -6glx + glx2 = 3glx + -3glx

Combine like terms: 3glx + -3glx = 0
8gl + -6glx + glx2 = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(8 + -6x + x2) = 0

Factor a trinomial.
gl((2 + -1x)(4 + -1x)) = 0


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

Simplifying
gl = 0

Solving
gl = 0

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

Simplifying
gl = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing g 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

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Add 'x' to each side of the equation.
-1x + x = -4 + x

Combine like terms: -1x + x = 0
0 = -4 + x

Simplifying
0 = -4 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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