F(x)=8xln(5x)-8x

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Solution for F(x)=8xln(5x)-8x equation: 


Simplifying
F(x) = 8xln(5x) + -8x

Multiply F * x
xF = 8xln(5x) + -8x

Remove parenthesis around (5x)
xF = 8lnx * 5x + -8x

Reorder the terms for easier multiplication:
xF = 8 * 5lnx * x + -8x

Multiply 8 * 5
xF = 40lnx * x + -8x

Multiply lnx * x
xF = 40lnx2 + -8x

Solving
xF = 40lnx2 + -8x

Solving for variable 'x'.

Reorder the terms:
-40lnx2 + 8x + xF = 40lnx2 + -8x + -40lnx2 + 8x

Reorder the terms:
-40lnx2 + 8x + xF = 40lnx2 + -40lnx2 + -8x + 8x

Combine like terms: 40lnx2 + -40lnx2 = 0
-40lnx2 + 8x + xF = 0 + -8x + 8x
-40lnx2 + 8x + xF = -8x + 8x

Combine like terms: -8x + 8x = 0
-40lnx2 + 8x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-40lnx + 8 + 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 '(-40lnx + 8 + F)' equal to zero and attempt to solve:

Simplifying
-40lnx + 8 + F = 0

Reorder the terms:
8 + F + -40lnx = 0

Solving
8 + F + -40lnx = 0

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

Add '-8' to each side of the equation.
8 + F + -8 + -40lnx = 0 + -8

Reorder the terms:
8 + -8 + F + -40lnx = 0 + -8

Combine like terms: 8 + -8 = 0
0 + F + -40lnx = 0 + -8
F + -40lnx = 0 + -8

Combine like terms: 0 + -8 = -8
F + -40lnx = -8

Add '-1F' to each side of the equation.
F + -1F + -40lnx = -8 + -1F

Combine like terms: F + -1F = 0
0 + -40lnx = -8 + -1F
-40lnx = -8 + -1F

Divide each side by '-40ln'.
x = 0.2l-1n-1 + 0.025l-1n-1F

Simplifying
x = 0.2l-1n-1 + 0.025l-1n-1F
Solution
x = {0, 0.2l-1n-1 + 0.025l-1n-1F}

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