lg(7x-9)=lg(6-x)

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Solution for lg(7x-9)=lg(6-x) equation: 


Simplifying
lg(7x + -9) = lg(6 + -1x)

Reorder the terms:
gl(-9 + 7x) = lg(6 + -1x)
(-9 * gl + 7x * gl) = lg(6 + -1x)
(-9gl + 7glx) = lg(6 + -1x)
-9gl + 7glx = (6 * gl + -1x * gl)
-9gl + 7glx = (6gl + -1glx)

Solving
-9gl + 7glx = 6gl + -1glx

Solving for variable 'g'.

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

Add '-6gl' to each side of the equation.
-9gl + -6gl + 7glx = 6gl + -6gl + -1glx

Combine like terms: -9gl + -6gl = -15gl
-15gl + 7glx = 6gl + -6gl + -1glx

Combine like terms: 6gl + -6gl = 0
-15gl + 7glx = 0 + -1glx
-15gl + 7glx = -1glx

Add 'glx' to each side of the equation.
-15gl + 7glx + glx = -1glx + glx

Combine like terms: 7glx + glx = 8glx
-15gl + 8glx = -1glx + glx

Combine like terms: -1glx + glx = 0
-15gl + 8glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-15 + 8x) = 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 '(-15 + 8x)' equal to zero and attempt to solve:

Simplifying
-15 + 8x = 0

Solving
-15 + 8x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 8x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8x = 0 + 15
8x = 0 + 15

Combine like terms: 0 + 15 = 15
8x = 15

Add '-8x' to each side of the equation.
8x + -8x = 15 + -8x

Combine like terms: 8x + -8x = 0
0 = 15 + -8x

Simplifying
0 = 15 + -8x

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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