Ln(2x-3)+2ln(x-2)=ln(-2x^2+19x-24)

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Solution for Ln(2x-3)+2ln(x-2)=ln(-2x^2+19x-24) equation: 


Simplifying
Ln(2x + -3) + 2ln(x + -2) = ln(-2x2 + 19x + -24)

Reorder the terms:
nL(-3 + 2x) + 2ln(x + -2) = ln(-2x2 + 19x + -24)
(-3 * nL + 2x * nL) + 2ln(x + -2) = ln(-2x2 + 19x + -24)
(-3nL + 2nxL) + 2ln(x + -2) = ln(-2x2 + 19x + -24)

Reorder the terms:
-3nL + 2nxL + 2ln(-2 + x) = ln(-2x2 + 19x + -24)
-3nL + 2nxL + (-2 * 2ln + x * 2ln) = ln(-2x2 + 19x + -24)
-3nL + 2nxL + (-4ln + 2lnx) = ln(-2x2 + 19x + -24)

Reorder the terms:
-4ln + 2lnx + -3nL + 2nxL = ln(-2x2 + 19x + -24)

Reorder the terms:
-4ln + 2lnx + -3nL + 2nxL = ln(-24 + 19x + -2x2)
-4ln + 2lnx + -3nL + 2nxL = (-24 * ln + 19x * ln + -2x2 * ln)
-4ln + 2lnx + -3nL + 2nxL = (-24ln + 19lnx + -2lnx2)

Solving
-4ln + 2lnx + -3nL + 2nxL = -24ln + 19lnx + -2lnx2

Solving for variable 'l'.

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

Add '24ln' to each side of the equation.
-4ln + 2lnx + -3nL + 24ln + 2nxL = -24ln + 19lnx + 24ln + -2lnx2

Reorder the terms:
-4ln + 24ln + 2lnx + -3nL + 2nxL = -24ln + 19lnx + 24ln + -2lnx2

Combine like terms: -4ln + 24ln = 20ln
20ln + 2lnx + -3nL + 2nxL = -24ln + 19lnx + 24ln + -2lnx2

Reorder the terms:
20ln + 2lnx + -3nL + 2nxL = -24ln + 24ln + 19lnx + -2lnx2

Combine like terms: -24ln + 24ln = 0
20ln + 2lnx + -3nL + 2nxL = 0 + 19lnx + -2lnx2
20ln + 2lnx + -3nL + 2nxL = 19lnx + -2lnx2

Add '-19lnx' to each side of the equation.
20ln + 2lnx + -3nL + -19lnx + 2nxL = 19lnx + -19lnx + -2lnx2

Reorder the terms:
20ln + 2lnx + -19lnx + -3nL + 2nxL = 19lnx + -19lnx + -2lnx2

Combine like terms: 2lnx + -19lnx = -17lnx
20ln + -17lnx + -3nL + 2nxL = 19lnx + -19lnx + -2lnx2

Combine like terms: 19lnx + -19lnx = 0
20ln + -17lnx + -3nL + 2nxL = 0 + -2lnx2
20ln + -17lnx + -3nL + 2nxL = -2lnx2

Add '2lnx2' to each side of the equation.
20ln + -17lnx + -3nL + 2lnx2 + 2nxL = -2lnx2 + 2lnx2

Reorder the terms:
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = -2lnx2 + 2lnx2

Combine like terms: -2lnx2 + 2lnx2 = 0
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = 0

Add '3nL' to each side of the equation.
20ln + -17lnx + 2lnx2 + -3nL + 3nL + 2nxL = 0 + 3nL

Combine like terms: -3nL + 3nL = 0
20ln + -17lnx + 2lnx2 + 0 + 2nxL = 0 + 3nL
20ln + -17lnx + 2lnx2 + 2nxL = 0 + 3nL
Remove the zero:
20ln + -17lnx + 2lnx2 + 2nxL = 3nL

Add '-2nxL' to each side of the equation.
20ln + -17lnx + 2lnx2 + 2nxL + -2nxL = 3nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
20ln + -17lnx + 2lnx2 + 0 = 3nL + -2nxL
20ln + -17lnx + 2lnx2 = 3nL + -2nxL

Reorder the terms:
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = 3nL + -3nL + -2nxL + 2nxL

Combine like terms: 3nL + -3nL = 0
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = 0 + -2nxL + 2nxL
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
20ln + -17lnx + 2lnx2 + -3nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(20l + -17lx + 2lx2 + -3L + 2xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(20l + -17lx + 2lx2 + -3L + 2xL)' equal to zero and attempt to solve:

Simplifying
20l + -17lx + 2lx2 + -3L + 2xL = 0

Reorder the terms:
-3L + 20l + -17lx + 2lx2 + 2xL = 0

Solving
-3L + 20l + -17lx + 2lx2 + 2xL = 0

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

Add '3L' to each side of the equation.
-3L + 20l + -17lx + 2lx2 + 3L + 2xL = 0 + 3L

Reorder the terms:
-3L + 3L + 20l + -17lx + 2lx2 + 2xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + 20l + -17lx + 2lx2 + 2xL = 0 + 3L
20l + -17lx + 2lx2 + 2xL = 0 + 3L
Remove the zero:
20l + -17lx + 2lx2 + 2xL = 3L

Add '-2xL' to each side of the equation.
20l + -17lx + 2lx2 + 2xL + -2xL = 3L + -2xL

Combine like terms: 2xL + -2xL = 0
20l + -17lx + 2lx2 + 0 = 3L + -2xL
20l + -17lx + 2lx2 = 3L + -2xL

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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