ln(x^2+2x)=ln(36-3x)

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Solution for ln(x^2+2x)=ln(36-3x) equation: 


Simplifying
ln(x2 + 2x) = ln(36 + -3x)

Reorder the terms:
ln(2x + x2) = ln(36 + -3x)
(2x * ln + x2 * ln) = ln(36 + -3x)
(2lnx + lnx2) = ln(36 + -3x)
2lnx + lnx2 = (36 * ln + -3x * ln)
2lnx + lnx2 = (36ln + -3lnx)

Solving
2lnx + lnx2 = 36ln + -3lnx

Solving for variable 'l'.

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

Add '-36ln' to each side of the equation.
2lnx + -36ln + lnx2 = 36ln + -36ln + -3lnx

Reorder the terms:
-36ln + 2lnx + lnx2 = 36ln + -36ln + -3lnx

Combine like terms: 36ln + -36ln = 0
-36ln + 2lnx + lnx2 = 0 + -3lnx
-36ln + 2lnx + lnx2 = -3lnx

Add '3lnx' to each side of the equation.
-36ln + 2lnx + 3lnx + lnx2 = -3lnx + 3lnx

Combine like terms: 2lnx + 3lnx = 5lnx
-36ln + 5lnx + lnx2 = -3lnx + 3lnx

Combine like terms: -3lnx + 3lnx = 0
-36ln + 5lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-36 + 5x + x2) = 0

Factor a trinomial.
ln((-9 + -1x)(4 + -1x)) = 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 '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Add 'x' to each side of the equation.
-1x + x = 9 + x

Combine like terms: -1x + x = 0
0 = 9 + x

Simplifying
0 = 9 + x

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Add 'x' to each side of the equation.
-1x + x = -4 + x

Combine like terms: -1x + x = 0
0 = -4 + x

Simplifying
0 = -4 + x

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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