(lnx-5)(lnx+3)=0

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Solution for (lnx-5)(lnx+3)=0 equation: 


Simplifying
(lnx + -5)(lnx + 3) = 0

Reorder the terms:
(-5 + lnx)(lnx + 3) = 0

Reorder the terms:
(-5 + lnx)(3 + lnx) = 0

Multiply (-5 + lnx) * (3 + lnx)
(-5(3 + lnx) + lnx(3 + lnx)) = 0
((3 * -5 + lnx * -5) + lnx(3 + lnx)) = 0
((-15 + -5lnx) + lnx(3 + lnx)) = 0
(-15 + -5lnx + (3 * lnx + lnx * lnx)) = 0
(-15 + -5lnx + (3lnx + l2n2x2)) = 0

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

Solving
-15 + -2lnx + l2n2x2 = 0

Solving for variable 'l'.

Factor a trinomial.
(-3 + -1lnx)(5 + -1lnx) = 0


Subproblem 1
Set the factor '(-3 + -1lnx)' equal to zero and attempt to solve:

Simplifying
-3 + -1lnx = 0

Solving
-3 + -1lnx = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -1lnx = 0 + 3
-1lnx = 0 + 3

Combine like terms: 0 + 3 = 3
-1lnx = 3

Divide each side by '-1nx'.
l = -3n-1x-1

Simplifying
l = -3n-1x-1

Subproblem 2
Set the factor '(5 + -1lnx)' equal to zero and attempt to solve:

Simplifying
5 + -1lnx = 0

Solving
5 + -1lnx = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1lnx = 0 + -5

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

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

Divide each side by '-1nx'.
l = 5n-1x-1

Simplifying
l = 5n-1x-1
Solution
l = {-3n-1x-1, 5n-1x-1}

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