Ln(x-7)(x+7)=ln(7)

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Solution for Ln(x-7)(x+7)=ln(7) equation: 


Simplifying
Ln(x + -7)(x + 7) = ln(7)

Reorder the terms:
nL(-7 + x)(x + 7) = ln(7)

Reorder the terms:
nL(-7 + x)(7 + x) = ln(7)

Multiply (-7 + x) * (7 + x)
nL(-7(7 + x) + x(7 + x)) = ln(7)
nL((7 * -7 + x * -7) + x(7 + x)) = ln(7)
nL((-49 + -7x) + x(7 + x)) = ln(7)
nL(-49 + -7x + (7 * x + x * x)) = ln(7)
nL(-49 + -7x + (7x + x2)) = ln(7)

Combine like terms: -7x + 7x = 0
nL(-49 + 0 + x2) = ln(7)
nL(-49 + x2) = ln(7)
(-49 * nL + x2 * nL) = ln(7)
(-49nL + nx2L) = ln(7)

Reorder the terms for easier multiplication:
-49nL + nx2L = 7ln

Solving
-49nL + nx2L = 7ln

Solving for variable 'n'.

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

Add '-7ln' to each side of the equation.
-49nL + -7ln + nx2L = 7ln + -7ln

Reorder the terms:
-7ln + -49nL + nx2L = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-7ln + -49nL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-7l + -49L + x2L) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-7l + -49L + x2L)' equal to zero and attempt to solve:

Simplifying
-7l + -49L + x2L = 0

Reorder the terms:
-49L + -7l + x2L = 0

Solving
-49L + -7l + x2L = 0

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

Add '49L' to each side of the equation.
-49L + -7l + 49L + x2L = 0 + 49L

Reorder the terms:
-49L + 49L + -7l + x2L = 0 + 49L

Combine like terms: -49L + 49L = 0
0 + -7l + x2L = 0 + 49L
-7l + x2L = 0 + 49L
Remove the zero:
-7l + x2L = 49L

Add '7l' to each side of the equation.
-7l + 7l + x2L = 49L + 7l

Combine like terms: -7l + 7l = 0
0 + x2L = 49L + 7l
x2L = 49L + 7l

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 49L + 7l + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 49L + 7l + -1x2L

Simplifying
0 = 49L + 7l + -1x2L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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