F(x)=(3x+7)lnx

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Solution for F(x)=(3x+7)lnx equation: 


Simplifying
F(x) = (3x + 7) * lnx

Multiply F * x
xF = (3x + 7) * lnx

Reorder the terms:
xF = (7 + 3x) * lnx

Reorder the terms for easier multiplication:
xF = lnx(7 + 3x)
xF = (7 * lnx + 3x * lnx)
xF = (7lnx + 3lnx2)

Solving
xF = 7lnx + 3lnx2

Solving for variable 'x'.

Reorder the terms:
-7lnx + -3lnx2 + xF = 7lnx + 3lnx2 + -7lnx + -3lnx2

Reorder the terms:
-7lnx + -3lnx2 + xF = 7lnx + -7lnx + 3lnx2 + -3lnx2

Combine like terms: 7lnx + -7lnx = 0
-7lnx + -3lnx2 + xF = 0 + 3lnx2 + -3lnx2
-7lnx + -3lnx2 + xF = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
-7lnx + -3lnx2 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7ln + -3lnx + 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 '(-7ln + -3lnx + F)' equal to zero and attempt to solve:

Simplifying
-7ln + -3lnx + F = 0

Reorder the terms:
F + -7ln + -3lnx = 0

Solving
F + -7ln + -3lnx = 0

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

Add '-1F' to each side of the equation.
F + -7ln + -1F + -3lnx = 0 + -1F

Reorder the terms:
F + -1F + -7ln + -3lnx = 0 + -1F

Combine like terms: F + -1F = 0
0 + -7ln + -3lnx = 0 + -1F
-7ln + -3lnx = 0 + -1F
Remove the zero:
-7ln + -3lnx = -1F

Add '7ln' to each side of the equation.
-7ln + 7ln + -3lnx = -1F + 7ln

Combine like terms: -7ln + 7ln = 0
0 + -3lnx = -1F + 7ln
-3lnx = -1F + 7ln

Divide each side by '-3ln'.
x = 0.3333333333l-1n-1F + -2.333333333

Simplifying
x = 0.3333333333l-1n-1F + -2.333333333

Reorder the terms:
x = -2.333333333 + 0.3333333333l-1n-1F
Solution
x = {0, -2.333333333 + 0.3333333333l-1n-1F}

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