lg(x^2+2x-3)=Lg(x-3)

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


Simplifying
lg(x2 + 2x + -3) = Lg(x + -3)

Reorder the terms:
gl(-3 + 2x + x2) = Lg(x + -3)
(-3 * gl + 2x * gl + x2 * gl) = Lg(x + -3)
(-3gl + 2glx + glx2) = Lg(x + -3)

Reorder the terms:
-3gl + 2glx + glx2 = gL(-3 + x)
-3gl + 2glx + glx2 = (-3 * gL + x * gL)
-3gl + 2glx + glx2 = (-3gL + gxL)

Solving
-3gl + 2glx + glx2 = -3gL + gxL

Solving for variable 'g'.

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

Add '3gL' to each side of the equation.
-3gl + 2glx + 3gL + glx2 = -3gL + 3gL + gxL

Reorder the terms:
3gL + -3gl + 2glx + glx2 = -3gL + 3gL + gxL

Combine like terms: -3gL + 3gL = 0
3gL + -3gl + 2glx + glx2 = 0 + gxL
3gL + -3gl + 2glx + glx2 = gxL

Add '-1gxL' to each side of the equation.
3gL + -3gl + 2glx + glx2 + -1gxL = gxL + -1gxL

Combine like terms: gxL + -1gxL = 0
3gL + -3gl + 2glx + glx2 + -1gxL = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(3L + -3l + 2lx + lx2 + -1xL) = 0


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

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0

Subproblem 2
Set the factor '(3L + -3l + 2lx + lx2 + -1xL)' equal to zero and attempt to solve:

Simplifying
3L + -3l + 2lx + lx2 + -1xL = 0

Solving
3L + -3l + 2lx + lx2 + -1xL = 0

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

Add '-3L' to each side of the equation.
3L + -3l + 2lx + lx2 + -3L + -1xL = 0 + -3L

Reorder the terms:
3L + -3L + -3l + 2lx + lx2 + -1xL = 0 + -3L

Combine like terms: 3L + -3L = 0
0 + -3l + 2lx + lx2 + -1xL = 0 + -3L
-3l + 2lx + lx2 + -1xL = 0 + -3L
Remove the zero:
-3l + 2lx + lx2 + -1xL = -3L

Add '3l' to each side of the equation.
-3l + 2lx + lx2 + 3l + -1xL = -3L + 3l

Reorder the terms:
-3l + 3l + 2lx + lx2 + -1xL = -3L + 3l

Combine like terms: -3l + 3l = 0
0 + 2lx + lx2 + -1xL = -3L + 3l
2lx + lx2 + -1xL = -3L + 3l

Add '-2lx' to each side of the equation.
2lx + lx2 + -2lx + -1xL = -3L + 3l + -2lx

Reorder the terms:
2lx + -2lx + lx2 + -1xL = -3L + 3l + -2lx

Combine like terms: 2lx + -2lx = 0
0 + lx2 + -1xL = -3L + 3l + -2lx
lx2 + -1xL = -3L + 3l + -2lx

Add '-1lx2' to each side of the equation.
lx2 + -1lx2 + -1xL = -3L + 3l + -2lx + -1lx2

Combine like terms: lx2 + -1lx2 = 0
0 + -1xL = -3L + 3l + -2lx + -1lx2
-1xL = -3L + 3l + -2lx + -1lx2

Add 'xL' to each side of the equation.
-1xL + xL = -3L + 3l + -2lx + -1lx2 + xL

Combine like terms: -1xL + xL = 0
0 = -3L + 3l + -2lx + -1lx2 + xL

Simplifying
0 = -3L + 3l + -2lx + -1lx2 + xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
g = {0}

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