log(5x^2+8)-log(14x)=0

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Solution for log(5x^2+8)-log(14x)=0 equation:


Simplifying
log(5x2 + 8) + -1log(14x) = 0

Reorder the terms:
glo(8 + 5x2) + -1log(14x) = 0
(8 * glo + 5x2 * glo) + -1log(14x) = 0
(8glo + 5glox2) + -1log(14x) = 0

Remove parenthesis around (14x)
8glo + 5glox2 + -1glo * 14x = 0

Reorder the terms for easier multiplication:
8glo + 5glox2 + -1 * 14glo * x = 0

Multiply -1 * 14
8glo + 5glox2 + -14glo * x = 0

Multiply glo * x
8glo + 5glox2 + -14glox = 0

Reorder the terms:
8glo + -14glox + 5glox2 = 0

Solving
8glo + -14glox + 5glox2 = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(8 + -14x + 5x2) = 0

Factor a trinomial.
glo((4 + -5x)(2 + -1x)) = 0

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Add '5x' to each side of the equation. -5x + 5x = -4 + 5x Combine like terms: -5x + 5x = 0 0 = -4 + 5x Simplifying 0 = -4 + 5x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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