7+6lnx(3x-2)=13

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Solution for 7+6lnx(3x-2)=13 equation: 


Simplifying
7 + 6lnx(3x + -2) = 13

Reorder the terms:
7 + 6lnx(-2 + 3x) = 13
7 + (-2 * 6lnx + 3x * 6lnx) = 13
7 + (-12lnx + 18lnx2) = 13

Solving
7 + -12lnx + 18lnx2 = 13

Solving for variable 'l'.

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

Add '-7' to each side of the equation.
7 + -12lnx + -7 + 18lnx2 = 13 + -7

Reorder the terms:
7 + -7 + -12lnx + 18lnx2 = 13 + -7

Combine like terms: 7 + -7 = 0
0 + -12lnx + 18lnx2 = 13 + -7
-12lnx + 18lnx2 = 13 + -7

Combine like terms: 13 + -7 = 6
-12lnx + 18lnx2 = 6

Reorder the terms:
-6 + -12lnx + 18lnx2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -12lnx + 18lnx2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -2lnx + 3lnx2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-1 + -2lnx + 3lnx2)' equal to zero and attempt to solve:

Simplifying
-1 + -2lnx + 3lnx2 = 0

Solving
-1 + -2lnx + 3lnx2 = 0

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

Add '1' to each side of the equation.
-1 + -2lnx + 1 + 3lnx2 = 0 + 1

Reorder the terms:
-1 + 1 + -2lnx + 3lnx2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2lnx + 3lnx2 = 0 + 1
-2lnx + 3lnx2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2lnx + 3lnx2 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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