2xln(0.25x)+x=0

Solution for 2xln(0.25x)+x=0 equation:

Simplifying
2xln(0.25x) + x = 0

Remove parenthesis around (0.25x)
2lnx * 0.25x + x = 0

Reorder the terms for easier multiplication:
2 * 0.25lnx * x + x = 0

Multiply 2 * 0.25
0.5lnx * x + x = 0

Multiply lnx * x
0.5lnx2 + x = 0

Solving
0.5lnx2 + x = 0

Solving for variable 'l'.

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

Add '-1x' to each side of the equation.
0.5lnx2 + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
0.5lnx2 + 0 = 0 + -1x
0.5lnx2 = 0 + -1x
Remove the zero:
0.5lnx2 = -1x

Divide each side by '0.5nx2'.
l = -2n-1x-1

Simplifying
l = -2n-1x-1