x=3ln(x^2+5x)

Solution for x=3ln(x^2+5x) equation:

Simplifying
x = 3ln(x2 + 5x)

Reorder the terms:
x = 3ln(5x + x2)
x = (5x * 3ln + x2 * 3ln)
x = (15lnx + 3lnx2)

Solving
x = 15lnx + 3lnx2

Solving for variable 'x'.

Reorder the terms:
-15lnx + -3lnx2 + x = 15lnx + 3lnx2 + -15lnx + -3lnx2

Reorder the terms:
-15lnx + -3lnx2 + x = 15lnx + -15lnx + 3lnx2 + -3lnx2

Combine like terms: 15lnx + -15lnx = 0
-15lnx + -3lnx2 + x = 0 + 3lnx2 + -3lnx2
-15lnx + -3lnx2 + x = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
-15lnx + -3lnx2 + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15ln + -3lnx + 1) = 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 '(-15ln + -3lnx + 1)' equal to zero and attempt to solve:

Simplifying
-15ln + -3lnx + 1 = 0

Reorder the terms:
1 + -15ln + -3lnx = 0

Solving
1 + -15ln + -3lnx = 0

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

Add '-1' to each side of the equation.
1 + -15ln + -1 + -3lnx = 0 + -1

Reorder the terms:
1 + -1 + -15ln + -3lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -15ln + -3lnx = 0 + -1
-15ln + -3lnx = 0 + -1

Combine like terms: 0 + -1 = -1
-15ln + -3lnx = -1

Add '15ln' to each side of the equation.
-15ln + 15ln + -3lnx = -1 + 15ln

Combine like terms: -15ln + 15ln = 0
0 + -3lnx = -1 + 15ln
-3lnx = -1 + 15ln

Divide each side by '-3ln'.
x = 0.3333333333l-1n-1 + -5

Simplifying
x = 0.3333333333l-1n-1 + -5

Reorder the terms:
x = -5 + 0.3333333333l-1n-1
Solution
x = {0, -5 + 0.3333333333l-1n-1}