lg(3x+2)-lg(9x^2+12x+4)=y

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Solution for lg(3x+2)-lg(9x^2+12x+4)=y equation: 


Simplifying
lg(3x + 2) + -1lg(9x2 + 12x + 4) = y

Reorder the terms:
gl(2 + 3x) + -1lg(9x2 + 12x + 4) = y
(2 * gl + 3x * gl) + -1lg(9x2 + 12x + 4) = y
(2gl + 3glx) + -1lg(9x2 + 12x + 4) = y

Reorder the terms:
2gl + 3glx + -1gl(4 + 12x + 9x2) = y
2gl + 3glx + (4 * -1gl + 12x * -1gl + 9x2 * -1gl) = y
2gl + 3glx + (-4gl + -12glx + -9glx2) = y

Reorder the terms:
2gl + -4gl + 3glx + -12glx + -9glx2 = y

Combine like terms: 2gl + -4gl = -2gl
-2gl + 3glx + -12glx + -9glx2 = y

Combine like terms: 3glx + -12glx = -9glx
-2gl + -9glx + -9glx2 = y

Solving
-2gl + -9glx + -9glx2 = y

Solving for variable 'g'.

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

Combine like terms: y + -1y = 0
-2gl + -9glx + -9glx2 + -1y = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2gl + 9glx + 9glx2 + y) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2gl + 9glx + 9glx2 + y)' equal to zero and attempt to solve:

Simplifying
2gl + 9glx + 9glx2 + y = 0

Solving
2gl + 9glx + 9glx2 + y = 0

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

Add '-1y' to each side of the equation.
2gl + 9glx + 9glx2 + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2gl + 9glx + 9glx2 + 0 = 0 + -1y
2gl + 9glx + 9glx2 = 0 + -1y
Remove the zero:
2gl + 9glx + 9glx2 = -1y

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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