log[3]x^2+log[3]x-3=0

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Solution for log[3]x^2+log[3]x-3=0 equation:


Simplifying
log[3] * x2 + log[3] * x + -3 = 0

Reorder the terms for easier multiplication:
3glo * x2 + log[3] * x + -3 = 0

Multiply glo * x2
3glox2 + log[3] * x + -3 = 0

Reorder the terms for easier multiplication:
3glox2 + 3glo * x + -3 = 0

Multiply glo * x
3glox2 + 3glox + -3 = 0

Reorder the terms:
-3 + 3glox + 3glox2 = 0

Solving
-3 + 3glox + 3glox2 = 0

Solving for variable 'g'.

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

Add '3' to each side of the equation.
-3 + 3glox + 3 + 3glox2 = 0 + 3

Reorder the terms:
-3 + 3 + 3glox + 3glox2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3glox + 3glox2 = 0 + 3
3glox + 3glox2 = 0 + 3

Combine like terms: 0 + 3 = 3
3glox + 3glox2 = 3

Reorder the terms:
-3 + 3glox + 3glox2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 3glox + 3glox2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + glox + glox2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + glox + glox2)' equal to zero and attempt to solve: Simplifying -1 + glox + glox2 = 0 Solving -1 + glox + glox2 = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + glox + 1 + glox2 = 0 + 1 Reorder the terms: -1 + 1 + glox + glox2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + glox + glox2 = 0 + 1 glox + glox2 = 0 + 1 Combine like terms: 0 + 1 = 1 glox + glox2 = 1 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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