2log(w)-(log(3))(w+7)=1

Solution for 2log(w)-(log(3))(w+7)=1 equation:

Simplifying
2log(w) + -1(log(3))(w + 7) = 1

Multiply glo * w
2glow + -1(log(3))(w + 7) = 1

Reorder the terms for easier multiplication:
2glow + -1(3glo)(w + 7) = 1

Remove parenthesis around (3glo)
2glow + -1 * 3glo(w + 7) = 1

Reorder the terms:
2glow + -1 * 3glo(7 + w) = 1

Multiply -1 * 3
2glow + -3glo(7 + w) = 1
2glow + (7 * -3glo + w * -3glo) = 1
2glow + (-21glo + -3glow) = 1

Reorder the terms:
-21glo + 2glow + -3glow = 1

Combine like terms: 2glow + -3glow = -1glow
-21glo + -1glow = 1

Solving
-21glo + -1glow = 1

Solving for variable 'g'.

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

Reorder the terms:
-1 + -21glo + -1glow = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -21glo + -1glow = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 21glo + glow) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 21glo + glow)' equal to zero and attempt to solve:

Simplifying
1 + 21glo + glow = 0

Solving
1 + 21glo + glow = 0

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

Add '-1' to each side of the equation.
1 + 21glo + -1 + glow = 0 + -1

Reorder the terms:
1 + -1 + 21glo + glow = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 21glo + glow = 0 + -1
21glo + glow = 0 + -1

Combine like terms: 0 + -1 = -1
21glo + glow = -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.