F(x)=x*ln(5x+3)

Solution for F(x)=x*ln(5x+3) equation:

Simplifying
F(x) = x * ln(5x + 3)

Multiply F * x
xF = x * ln(5x + 3)

Reorder the terms:
xF = x * ln(3 + 5x)

Multiply x * ln
xF = lnx(3 + 5x)
xF = (3 * lnx + 5x * lnx)
xF = (3lnx + 5lnx2)

Solving
xF = 3lnx + 5lnx2

Solving for variable 'x'.

Reorder the terms:
-3lnx + -5lnx2 + xF = 3lnx + 5lnx2 + -3lnx + -5lnx2

Reorder the terms:
-3lnx + -5lnx2 + xF = 3lnx + -3lnx + 5lnx2 + -5lnx2

Combine like terms: 3lnx + -3lnx = 0
-3lnx + -5lnx2 + xF = 0 + 5lnx2 + -5lnx2
-3lnx + -5lnx2 + xF = 5lnx2 + -5lnx2

Combine like terms: 5lnx2 + -5lnx2 = 0
-3lnx + -5lnx2 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3ln + -5lnx + F) = 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 '(-3ln + -5lnx + F)' equal to zero and attempt to solve:

Simplifying
-3ln + -5lnx + F = 0

Reorder the terms:
F + -3ln + -5lnx = 0

Solving
F + -3ln + -5lnx = 0

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

Add '-1F' to each side of the equation.
F + -3ln + -1F + -5lnx = 0 + -1F

Reorder the terms:
F + -1F + -3ln + -5lnx = 0 + -1F

Combine like terms: F + -1F = 0
0 + -3ln + -5lnx = 0 + -1F
-3ln + -5lnx = 0 + -1F
Remove the zero:
-3ln + -5lnx = -1F

Add '3ln' to each side of the equation.
-3ln + 3ln + -5lnx = -1F + 3ln

Combine like terms: -3ln + 3ln = 0
0 + -5lnx = -1F + 3ln
-5lnx = -1F + 3ln

Divide each side by '-5ln'.
x = 0.2l-1n-1F + -0.6

Simplifying
x = 0.2l-1n-1F + -0.6

Reorder the terms:
x = -0.6 + 0.2l-1n-1F
Solution
x = {0, -0.6 + 0.2l-1n-1F}