log[5](3x-2)-log[5](5-x)=x^2-x-2

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Solution for log[5](3x-2)-log[5](5-x)=x^2-x-2 equation: 


Simplifying
log[5](3x + -2) + -1log[5](5 + -1x) = x2 + -1x + -2

Reorder the terms:
glo * 5(-2 + 3x) + -1log[5](5 + -1x) = x2 + -1x + -2

Reorder the terms for easier multiplication:
5glo(-2 + 3x) + -1log[5](5 + -1x) = x2 + -1x + -2
(-2 * 5glo + 3x * 5glo) + -1log[5](5 + -1x) = x2 + -1x + -2
(-10glo + 15glox) + -1log[5](5 + -1x) = x2 + -1x + -2

Reorder the terms for easier multiplication:
-10glo + 15glox + -1 * 5glo(5 + -1x) = x2 + -1x + -2

Multiply -1 * 5
-10glo + 15glox + -5glo(5 + -1x) = x2 + -1x + -2
-10glo + 15glox + (5 * -5glo + -1x * -5glo) = x2 + -1x + -2
-10glo + 15glox + (-25glo + 5glox) = x2 + -1x + -2

Reorder the terms:
-10glo + -25glo + 15glox + 5glox = x2 + -1x + -2

Combine like terms: -10glo + -25glo = -35glo
-35glo + 15glox + 5glox = x2 + -1x + -2

Combine like terms: 15glox + 5glox = 20glox
-35glo + 20glox = x2 + -1x + -2

Reorder the terms:
-35glo + 20glox = -2 + -1x + x2

Solving
-35glo + 20glox = -2 + -1x + x2

Solving for variable 'g'.

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

Reorder the terms:
2 + -35glo + 20glox + x + -1x2 = -2 + -1x + x2 + 2 + x + -1x2

Reorder the terms:
2 + -35glo + 20glox + x + -1x2 = -2 + 2 + -1x + x + x2 + -1x2

Combine like terms: -2 + 2 = 0
2 + -35glo + 20glox + x + -1x2 = 0 + -1x + x + x2 + -1x2
2 + -35glo + 20glox + x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
2 + -35glo + 20glox + x + -1x2 = 0 + x2 + -1x2
2 + -35glo + 20glox + x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -35glo + 20glox + x + -1x2 = 0

The solution to this equation could not be determined.

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