2x^2=ln(4x)

Solution for 2x^2=ln(4x) equation:

Simplifying
2x2 = ln(4x)

Remove parenthesis around (4x)
2x2 = ln * 4x

Reorder the terms for easier multiplication:
2x2 = 4ln * x

Multiply ln * x
2x2 = 4lnx

Solving
2x2 = 4lnx

Solving for variable 'x'.

Reorder the terms:
-4lnx + 2x2 = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-4lnx + 2x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-2ln + x)' equal to zero and attempt to solve:

Simplifying
-2ln + x = 0

Solving
-2ln + x = 0

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

Add '2ln' to each side of the equation.
-2ln + 2ln + x = 0 + 2ln

Combine like terms: -2ln + 2ln = 0
0 + x = 0 + 2ln
x = 0 + 2ln
Remove the zero:
x = 2ln

Simplifying
x = 2ln
Solution
x = {0, 2ln}