x^2=ln(3y(x))

Solution for x^2=ln(3y(x)) equation:

Simplifying
x2 = ln(3y(x))

Multiply y * x
x2 = ln(3xy)

Remove parenthesis around (3xy)
x2 = ln * 3xy

Reorder the terms for easier multiplication:
x2 = 3ln * xy

Multiply ln * xy
x2 = 3lnxy

Solving
x2 = 3lnxy

Solving for variable 'x'.

Reorder the terms:
-3lnxy + x2 = 3lnxy + -3lnxy

Combine like terms: 3lnxy + -3lnxy = 0
-3lnxy + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3lny + x) = 0

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 '(-3lny + x)' equal to zero and attempt to solve:

Simplifying
-3lny + x = 0

Solving
-3lny + x = 0

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

Add '3lny' to each side of the equation.
-3lny + 3lny + x = 0 + 3lny

Combine like terms: -3lny + 3lny = 0
0 + x = 0 + 3lny
x = 0 + 3lny
Remove the zero:
x = 3lny

Simplifying
x = 3lny
Solution
x = {0, 3lny}