lg(4x+3)=lg(2-3x)

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Solution for lg(4x+3)=lg(2-3x) equation: 


Simplifying
lg(4x + 3) = lg(2 + -3x)

Reorder the terms:
gl(3 + 4x) = lg(2 + -3x)
(3 * gl + 4x * gl) = lg(2 + -3x)
(3gl + 4glx) = lg(2 + -3x)
3gl + 4glx = (2 * gl + -3x * gl)
3gl + 4glx = (2gl + -3glx)

Solving
3gl + 4glx = 2gl + -3glx

Solving for variable 'g'.

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

Add '-2gl' to each side of the equation.
3gl + -2gl + 4glx = 2gl + -2gl + -3glx

Combine like terms: 3gl + -2gl = 1gl
1gl + 4glx = 2gl + -2gl + -3glx

Combine like terms: 2gl + -2gl = 0
1gl + 4glx = 0 + -3glx
1gl + 4glx = -3glx

Add '3glx' to each side of the equation.
1gl + 4glx + 3glx = -3glx + 3glx

Combine like terms: 4glx + 3glx = 7glx
1gl + 7glx = -3glx + 3glx

Combine like terms: -3glx + 3glx = 0
1gl + 7glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(1 + 7x) = 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 '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Add '-7x' to each side of the equation.
7x + -7x = -1 + -7x

Combine like terms: 7x + -7x = 0
0 = -1 + -7x

Simplifying
0 = -1 + -7x

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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