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

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


Simplifying
F(x) = ln(2x2 + 3x)

Multiply F * x
xF = ln(2x2 + 3x)

Reorder the terms:
xF = ln(3x + 2x2)
xF = (3x * ln + 2x2 * ln)
xF = (3lnx + 2lnx2)

Solving
xF = 3lnx + 2lnx2

Solving for variable 'x'.

Reorder the terms:
-3lnx + -2lnx2 + xF = 3lnx + 2lnx2 + -3lnx + -2lnx2

Reorder the terms:
-3lnx + -2lnx2 + xF = 3lnx + -3lnx + 2lnx2 + -2lnx2

Combine like terms: 3lnx + -3lnx = 0
-3lnx + -2lnx2 + xF = 0 + 2lnx2 + -2lnx2
-3lnx + -2lnx2 + xF = 2lnx2 + -2lnx2

Combine like terms: 2lnx2 + -2lnx2 = 0
-3lnx + -2lnx2 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3ln + -2lnx + 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 + -2lnx + F)' equal to zero and attempt to solve:

Simplifying
-3ln + -2lnx + F = 0

Reorder the terms:
F + -3ln + -2lnx = 0

Solving
F + -3ln + -2lnx = 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 + -2lnx = 0 + -1F

Reorder the terms:
F + -1F + -3ln + -2lnx = 0 + -1F

Combine like terms: F + -1F = 0
0 + -3ln + -2lnx = 0 + -1F
-3ln + -2lnx = 0 + -1F
Remove the zero:
-3ln + -2lnx = -1F

Add '3ln' to each side of the equation.
-3ln + 3ln + -2lnx = -1F + 3ln

Combine like terms: -3ln + 3ln = 0
0 + -2lnx = -1F + 3ln
-2lnx = -1F + 3ln

Divide each side by '-2ln'.
x = 0.5l-1n-1F + -1.5

Simplifying
x = 0.5l-1n-1F + -1.5

Reorder the terms:
x = -1.5 + 0.5l-1n-1F
Solution
x = {0, -1.5 + 0.5l-1n-1F}

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