R(x)=x(52-5lnx)

Solution for R(x)=x(52-5lnx) equation:

Simplifying
R(x) = x(52 + -5lnx)

Multiply R * x
xR = x(52 + -5lnx)
xR = (52 * x + -5lnx * x)

Reorder the terms:
xR = (-5lnx2 + 52x)
xR = (-5lnx2 + 52x)

Solving
xR = -5lnx2 + 52x

Solving for variable 'x'.

Reorder the terms:
5lnx2 + -52x + xR = -5lnx2 + 52x + 5lnx2 + -52x

Reorder the terms:
5lnx2 + -52x + xR = -5lnx2 + 5lnx2 + 52x + -52x

Combine like terms: -5lnx2 + 5lnx2 = 0
5lnx2 + -52x + xR = 0 + 52x + -52x
5lnx2 + -52x + xR = 52x + -52x

Combine like terms: 52x + -52x = 0
5lnx2 + -52x + xR = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5lnx + -52 + R) = 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 '(5lnx + -52 + R)' equal to zero and attempt to solve:

Simplifying
5lnx + -52 + R = 0

Reorder the terms:
-52 + R + 5lnx = 0

Solving
-52 + R + 5lnx = 0

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

Add '52' to each side of the equation.
-52 + R + 52 + 5lnx = 0 + 52

Reorder the terms:
-52 + 52 + R + 5lnx = 0 + 52

Combine like terms: -52 + 52 = 0
0 + R + 5lnx = 0 + 52
R + 5lnx = 0 + 52

Combine like terms: 0 + 52 = 52
R + 5lnx = 52

Add '-1R' to each side of the equation.
R + -1R + 5lnx = 52 + -1R

Combine like terms: R + -1R = 0
0 + 5lnx = 52 + -1R
5lnx = 52 + -1R

Divide each side by '5ln'.
x = 10.4l-1n-1 + -0.2l-1n-1R

Simplifying
x = 10.4l-1n-1 + -0.2l-1n-1R
Solution
x = {0, 10.4l-1n-1 + -0.2l-1n-1R}