ln(x^2+9x)=ln(-32-3n)

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Solution for ln(x^2+9x)=ln(-32-3n) equation: 


Simplifying
ln(x2 + 9x) = ln(-32 + -3n)

Reorder the terms:
ln(9x + x2) = ln(-32 + -3n)
(9x * ln + x2 * ln) = ln(-32 + -3n)
(9lnx + lnx2) = ln(-32 + -3n)
9lnx + lnx2 = (-32 * ln + -3n * ln)
9lnx + lnx2 = (-32ln + -3ln2)

Solving
9lnx + lnx2 = -32ln + -3ln2

Solving for variable 'l'.

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

Add '32ln' to each side of the equation.
9lnx + 32ln + lnx2 = -32ln + 32ln + -3ln2

Reorder the terms:
32ln + 9lnx + lnx2 = -32ln + 32ln + -3ln2

Combine like terms: -32ln + 32ln = 0
32ln + 9lnx + lnx2 = 0 + -3ln2
32ln + 9lnx + lnx2 = -3ln2

Add '3ln2' to each side of the equation.
32ln + 9lnx + lnx2 + 3ln2 = -3ln2 + 3ln2

Combine like terms: -3ln2 + 3ln2 = 0
32ln + 9lnx + lnx2 + 3ln2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(32 + 9x + x2 + 3n) = 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 '(32 + 9x + x2 + 3n)' equal to zero and attempt to solve:

Simplifying
32 + 9x + x2 + 3n = 0

Reorder the terms:
32 + 3n + 9x + x2 = 0

Solving
32 + 3n + 9x + x2 = 0

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

Add '-32' to each side of the equation.
32 + 3n + 9x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 3n + 9x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 3n + 9x + x2 = 0 + -32
3n + 9x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
3n + 9x + x2 = -32

Add '-3n' to each side of the equation.
3n + 9x + -3n + x2 = -32 + -3n

Reorder the terms:
3n + -3n + 9x + x2 = -32 + -3n

Combine like terms: 3n + -3n = 0
0 + 9x + x2 = -32 + -3n
9x + x2 = -32 + -3n

Add '-9x' to each side of the equation.
9x + -9x + x2 = -32 + -3n + -9x

Combine like terms: 9x + -9x = 0
0 + x2 = -32 + -3n + -9x
x2 = -32 + -3n + -9x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -32 + -3n + -9x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -32 + -3n + -9x + -1x2

Simplifying
0 = -32 + -3n + -9x + -1x2

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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