((lnx)+7)((lnx)-2)=0

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Solution for ((lnx)+7)((lnx)-2)=0 equation: 


Simplifying
((lnx) + 7)((lnx) + -2) = 0
(lnx + 7)((lnx) + -2) = 0

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

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

Multiply (7 + lnx) * (-2 + lnx)
(7(-2 + lnx) + lnx(-2 + lnx)) = 0
((-2 * 7 + lnx * 7) + lnx(-2 + lnx)) = 0
((-14 + 7lnx) + lnx(-2 + lnx)) = 0
(-14 + 7lnx + (-2 * lnx + lnx * lnx)) = 0
(-14 + 7lnx + (-2lnx + l2n2x2)) = 0

Combine like terms: 7lnx + -2lnx = 5lnx
(-14 + 5lnx + l2n2x2) = 0

Solving
-14 + 5lnx + l2n2x2 = 0

Solving for variable 'l'.

Factor a trinomial.
(-7 + -1lnx)(2 + -1lnx) = 0


Subproblem 1
Set the factor '(-7 + -1lnx)' equal to zero and attempt to solve:

Simplifying
-7 + -1lnx = 0

Solving
-7 + -1lnx = 0

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

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

Combine like terms: -7 + 7 = 0
0 + -1lnx = 0 + 7
-1lnx = 0 + 7

Combine like terms: 0 + 7 = 7
-1lnx = 7

Divide each side by '-1nx'.
l = -7n-1x-1

Simplifying
l = -7n-1x-1

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

Simplifying
2 + -1lnx = 0

Solving
2 + -1lnx = 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 + -1lnx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1lnx = 0 + -2
-1lnx = 0 + -2

Combine like terms: 0 + -2 = -2
-1lnx = -2

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

Simplifying
l = 2n-1x-1
Solution
l = {-7n-1x-1, 2n-1x-1}

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