0.5+p(1-ln(p))=0

Solution for 0.5+p(1-ln(p))=0 equation:

Simplifying
0.5 + p(1 + -1ln(p)) = 0

Multiply ln * p
0.5 + p(1 + -1lnp) = 0
0.5 + (1 * p + -1lnp * p) = 0

Reorder the terms:
0.5 + (-1lnp2 + 1p) = 0
0.5 + (-1lnp2 + 1p) = 0

Solving
0.5 + -1lnp2 + 1p = 0

Solving for variable 'l'.

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

Add '-0.5' to each side of the equation.
0.5 + -1lnp2 + -0.5 + 1p = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1lnp2 + 1p = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1lnp2 + 1p = 0 + -0.5
-1lnp2 + 1p = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1lnp2 + 1p = -0.5

Add '-1p' to each side of the equation.
-1lnp2 + 1p + -1p = -0.5 + -1p

Combine like terms: 1p + -1p = 0
-1lnp2 + 0 = -0.5 + -1p
-1lnp2 = -0.5 + -1p

Divide each side by '-1np2'.
l = 0.5n-1p-2 + n-1p-1

Simplifying
l = 0.5n-1p-2 + n-1p-1