5(1-lnx)(lnx-2)=0

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Solution for 5(1-lnx)(lnx-2)=0 equation: 


Simplifying
5(1 + -1lnx)(lnx + -2) = 0

Reorder the terms:
5(1 + -1lnx)(-2 + lnx) = 0

Multiply (1 + -1lnx) * (-2 + lnx)
5(1(-2 + lnx) + -1lnx * (-2 + lnx)) = 0
5((-2 * 1 + lnx * 1) + -1lnx * (-2 + lnx)) = 0
5((-2 + 1lnx) + -1lnx * (-2 + lnx)) = 0
5(-2 + 1lnx + (-2 * -1lnx + lnx * -1lnx)) = 0
5(-2 + 1lnx + (2lnx + -1l2n2x2)) = 0

Combine like terms: 1lnx + 2lnx = 3lnx
5(-2 + 3lnx + -1l2n2x2) = 0
(-2 * 5 + 3lnx * 5 + -1l2n2x2 * 5) = 0
(-10 + 15lnx + -5l2n2x2) = 0

Solving
-10 + 15lnx + -5l2n2x2 = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 3lnx + -1l2n2x2) = 0

Factor a trinomial.
5((-2 + lnx)(1 + -1lnx)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + lnx)' equal to zero and attempt to solve:

Simplifying
-2 + lnx = 0

Solving
-2 + lnx = 0

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

Add '2' to each side of the equation.
-2 + 2 + lnx = 0 + 2

Combine like terms: -2 + 2 = 0
0 + lnx = 0 + 2
lnx = 0 + 2

Combine like terms: 0 + 2 = 2
lnx = 2

Divide each side by 'nx'.
l = 2n-1x-1

Simplifying
l = 2n-1x-1

Subproblem 2
Set the factor '(1 + -1lnx)' equal to zero and attempt to solve:

Simplifying
1 + -1lnx = 0

Solving
1 + -1lnx = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1lnx = 0 + -1
-1lnx = 0 + -1

Combine like terms: 0 + -1 = -1
-1lnx = -1

Divide each side by '-1nx'.
l = n-1x-1

Simplifying
l = n-1x-1
Solution
l = {2n-1x-1, n-1x-1}

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