ln(x+9)+l(2x+9)=ln(180)

Solution for ln(x+9)+l(2x+9)=ln(180) equation:

Simplifying
ln(x + 9) + l(2x + 9) = ln(180)

Reorder the terms:
ln(9 + x) + l(2x + 9) = ln(180)
(9 * ln + x * ln) + l(2x + 9) = ln(180)
(9ln + lnx) + l(2x + 9) = ln(180)

Reorder the terms:
9ln + lnx + l(9 + 2x) = ln(180)
9ln + lnx + (9 * l + 2x * l) = ln(180)
9ln + lnx + (9l + 2lx) = ln(180)

Reorder the terms:
9l + 9ln + lnx + 2lx = ln(180)

Reorder the terms for easier multiplication:
9l + 9ln + lnx + 2lx = 180ln

Solving
9l + 9ln + lnx + 2lx = 180ln

Solving for variable 'l'.

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

Add '-180ln' to each side of the equation.
9l + 9ln + lnx + -180ln + 2lx = 180ln + -180ln

Reorder the terms:
9l + 9ln + -180ln + lnx + 2lx = 180ln + -180ln

Combine like terms: 9ln + -180ln = -171ln
9l + -171ln + lnx + 2lx = 180ln + -180ln

Combine like terms: 180ln + -180ln = 0
9l + -171ln + lnx + 2lx = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(9 + -171n + nx + 2x) = 0

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

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(9 + -171n + nx + 2x)' equal to zero and attempt to solve:

Simplifying
9 + -171n + nx + 2x = 0

Solving
9 + -171n + nx + 2x = 0

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

Add '-9' to each side of the equation.
9 + -171n + nx + -9 + 2x = 0 + -9

Reorder the terms:
9 + -9 + -171n + nx + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -171n + nx + 2x = 0 + -9
-171n + nx + 2x = 0 + -9

Combine like terms: 0 + -9 = -9
-171n + nx + 2x = -9

Add '171n' to each side of the equation.
-171n + nx + 171n + 2x = -9 + 171n

Reorder the terms:
-171n + 171n + nx + 2x = -9 + 171n

Combine like terms: -171n + 171n = 0
0 + nx + 2x = -9 + 171n
nx + 2x = -9 + 171n

Add '-1nx' to each side of the equation.
nx + -1nx + 2x = -9 + 171n + -1nx

Combine like terms: nx + -1nx = 0
0 + 2x = -9 + 171n + -1nx
2x = -9 + 171n + -1nx

Add '-2x' to each side of the equation.
2x + -2x = -9 + 171n + -1nx + -2x

Combine like terms: 2x + -2x = 0
0 = -9 + 171n + -1nx + -2x

Simplifying
0 = -9 + 171n + -1nx + -2x

The solution to this equation could not be determined.

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