2+3*ln(x)*ln(x)=7*ln(x)

Solution for 2+3*ln(x)*ln(x)=7*ln(x) equation:

Simplifying
2 + 3ln(x) * ln(x) = 7ln(x)

Multiply ln * x
2 + 3lnx * ln * x = 7ln(x)

Multiply lnx * ln
2 + 3l2n2x * x = 7ln(x)

Multiply l2n2x * x
2 + 3l2n2x2 = 7ln(x)

Multiply ln * x
2 + 3l2n2x2 = 7lnx

Solving
2 + 3l2n2x2 = 7lnx

Solving for variable 'l'.

Reorder the terms:
2 + -7lnx + 3l2n2x2 = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
2 + -7lnx + 3l2n2x2 = 0

Factor a trinomial.
(1 + -3lnx)(2 + -1lnx) = 0

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

Simplifying
1 + -3lnx = 0

Solving
1 + -3lnx = 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 + -3lnx = 0 + -1

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

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

Divide each side by '-3nx'.
l = 0.3333333333n-1x-1

Simplifying
l = 0.3333333333n-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 = {0.3333333333n-1x-1, 2n-1x-1}