lg*(x-2)+lg*(x+3)=lg*14

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Solution for lg*(x-2)+lg*(x+3)=lg*14 equation: 


Simplifying
lg(x + -2) + lg(x + 3) = lg * 14

Reorder the terms:
gl(-2 + x) + lg(x + 3) = lg * 14
(-2 * gl + x * gl) + lg(x + 3) = lg * 14
(-2gl + glx) + lg(x + 3) = lg * 14

Reorder the terms:
-2gl + glx + gl(3 + x) = lg * 14
-2gl + glx + (3 * gl + x * gl) = lg * 14
-2gl + glx + (3gl + glx) = lg * 14

Reorder the terms:
-2gl + 3gl + glx + glx = lg * 14

Combine like terms: -2gl + 3gl = 1gl
1gl + glx + glx = lg * 14

Combine like terms: glx + glx = 2glx
1gl + 2glx = lg * 14

Reorder the terms for easier multiplication:
1gl + 2glx = 14gl

Solving
1gl + 2glx = 14gl

Solving for variable 'g'.

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

Add '-14gl' to each side of the equation.
1gl + -14gl + 2glx = 14gl + -14gl

Combine like terms: 1gl + -14gl = -13gl
-13gl + 2glx = 14gl + -14gl

Combine like terms: 14gl + -14gl = 0
-13gl + 2glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-13 + 2x) = 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 '(-13 + 2x)' equal to zero and attempt to solve:

Simplifying
-13 + 2x = 0

Solving
-13 + 2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 2x = 0 + 13
2x = 0 + 13

Combine like terms: 0 + 13 = 13
2x = 13

Add '-2x' to each side of the equation.
2x + -2x = 13 + -2x

Combine like terms: 2x + -2x = 0
0 = 13 + -2x

Simplifying
0 = 13 + -2x

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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