0=lnx(1+2x)+x+1

Solution for 0=lnx(1+2x)+x+1 equation:

Simplifying
0 = lnx(1 + 2x) + x + 1
0 = (1 * lnx + 2x * lnx) + x + 1
0 = (1lnx + 2lnx2) + x + 1

Reorder the terms:
0 = 1 + 1lnx + 2lnx2 + x

Solving
0 = 1 + 1lnx + 2lnx2 + x

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
0 + -1lnx = 1 + 1lnx + 2lnx2 + -1lnx + x
Remove the zero:
-1lnx = 1 + 1lnx + 2lnx2 + -1lnx + x

Reorder the terms:
-1lnx = 1 + 1lnx + -1lnx + 2lnx2 + x

Combine like terms: 1lnx + -1lnx = 0
-1lnx = 1 + 0 + 2lnx2 + x
-1lnx = 1 + 2lnx2 + x

Add '-2lnx2' to each side of the equation.
-1lnx + -2lnx2 = 1 + 2lnx2 + -2lnx2 + x

Combine like terms: 2lnx2 + -2lnx2 = 0
-1lnx + -2lnx2 = 1 + 0 + x
-1lnx + -2lnx2 = 1 + x

Reorder the terms:
-1 + -1lnx + -2lnx2 + -1x = 1 + x + -1 + -1x

Reorder the terms:
-1 + -1lnx + -2lnx2 + -1x = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-1 + -1lnx + -2lnx2 + -1x = 0 + x + -1x
-1 + -1lnx + -2lnx2 + -1x = x + -1x

Combine like terms: x + -1x = 0
-1 + -1lnx + -2lnx2 + -1x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + lnx + 2lnx2 + x) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + lnx + 2lnx2 + x)' equal to zero and attempt to solve:

Simplifying
1 + lnx + 2lnx2 + x = 0

Solving
1 + lnx + 2lnx2 + x = 0

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

Add '-1' to each side of the equation.
1 + lnx + 2lnx2 + -1 + x = 0 + -1

Reorder the terms:
1 + -1 + lnx + 2lnx2 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + lnx + 2lnx2 + x = 0 + -1
lnx + 2lnx2 + x = 0 + -1

Combine like terms: 0 + -1 = -1
lnx + 2lnx2 + x = -1

Add '-1x' to each side of the equation.
lnx + 2lnx2 + x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
lnx + 2lnx2 + 0 = -1 + -1x
lnx + 2lnx2 = -1 + -1x

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.