Ln(3x+1)ln(2x-3)=ln(10)

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Solution for Ln(3x+1)ln(2x-3)=ln(10) equation: 


Simplifying
Ln(3x + 1) * ln(2x + -3) = ln(10)

Reorder the terms:
nL(1 + 3x) * ln(2x + -3) = ln(10)

Reorder the terms:
nL(1 + 3x) * ln(-3 + 2x) = ln(10)

Reorder the terms for easier multiplication:
nL * ln(1 + 3x)(-3 + 2x) = ln(10)

Multiply nL * ln
ln2L(1 + 3x)(-3 + 2x) = ln(10)

Multiply (1 + 3x) * (-3 + 2x)
ln2L(1(-3 + 2x) + 3x * (-3 + 2x)) = ln(10)
ln2L((-3 * 1 + 2x * 1) + 3x * (-3 + 2x)) = ln(10)
ln2L((-3 + 2x) + 3x * (-3 + 2x)) = ln(10)
ln2L(-3 + 2x + (-3 * 3x + 2x * 3x)) = ln(10)
ln2L(-3 + 2x + (-9x + 6x2)) = ln(10)

Combine like terms: 2x + -9x = -7x
ln2L(-3 + -7x + 6x2) = ln(10)
(-3 * ln2L + -7x * ln2L + 6x2 * ln2L) = ln(10)
(-3ln2L + -7ln2xL + 6ln2x2L) = ln(10)

Reorder the terms for easier multiplication:
-3ln2L + -7ln2xL + 6ln2x2L = 10ln

Solving
-3ln2L + -7ln2xL + 6ln2x2L = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-3ln2L + -7ln2xL + -10ln + 6ln2x2L = 10ln + -10ln

Reorder the terms:
-10ln + -3ln2L + -7ln2xL + 6ln2x2L = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-10ln + -3ln2L + -7ln2xL + 6ln2x2L = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-10 + -3nL + -7nxL + 6nx2L) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-10 + -3nL + -7nxL + 6nx2L)' equal to zero and attempt to solve:

Simplifying
-10 + -3nL + -7nxL + 6nx2L = 0

Solving
-10 + -3nL + -7nxL + 6nx2L = 0

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

Add '10' to each side of the equation.
-10 + -3nL + -7nxL + 10 + 6nx2L = 0 + 10

Reorder the terms:
-10 + 10 + -3nL + -7nxL + 6nx2L = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3nL + -7nxL + 6nx2L = 0 + 10
-3nL + -7nxL + 6nx2L = 0 + 10

Combine like terms: 0 + 10 = 10
-3nL + -7nxL + 6nx2L = 10

Add '3nL' to each side of the equation.
-3nL + -7nxL + 3nL + 6nx2L = 10 + 3nL

Reorder the terms:
-3nL + 3nL + -7nxL + 6nx2L = 10 + 3nL

Combine like terms: -3nL + 3nL = 0
0 + -7nxL + 6nx2L = 10 + 3nL
-7nxL + 6nx2L = 10 + 3nL

Add '7nxL' to each side of the equation.
-7nxL + 7nxL + 6nx2L = 10 + 3nL + 7nxL

Combine like terms: -7nxL + 7nxL = 0
0 + 6nx2L = 10 + 3nL + 7nxL
6nx2L = 10 + 3nL + 7nxL

Add '-6nx2L' to each side of the equation.
6nx2L + -6nx2L = 10 + 3nL + 7nxL + -6nx2L

Combine like terms: 6nx2L + -6nx2L = 0
0 = 10 + 3nL + 7nxL + -6nx2L

Simplifying
0 = 10 + 3nL + 7nxL + -6nx2L

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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