On(3x-3)=on(x-6)

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Solution for On(3x-3)=on(x-6) equation: 


Simplifying
On(3x + -3) = on(x + -6)

Reorder the terms:
nO(-3 + 3x) = on(x + -6)
(-3 * nO + 3x * nO) = on(x + -6)
(-3nO + 3nxO) = on(x + -6)

Reorder the terms:
-3nO + 3nxO = no(-6 + x)
-3nO + 3nxO = (-6 * no + x * no)
-3nO + 3nxO = (-6no + nox)

Solving
-3nO + 3nxO = -6no + nox

Solving for variable 'n'.

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

Add '6no' to each side of the equation.
-3nO + 6no + 3nxO = -6no + 6no + nox

Combine like terms: -6no + 6no = 0
-3nO + 6no + 3nxO = 0 + nox
-3nO + 6no + 3nxO = nox

Add '-1nox' to each side of the equation.
-3nO + 6no + -1nox + 3nxO = nox + -1nox

Combine like terms: nox + -1nox = 0
-3nO + 6no + -1nox + 3nxO = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3O + 6o + -1ox + 3xO) = 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 '(-3O + 6o + -1ox + 3xO)' equal to zero and attempt to solve:

Simplifying
-3O + 6o + -1ox + 3xO = 0

Solving
-3O + 6o + -1ox + 3xO = 0

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

Add '3O' to each side of the equation.
-3O + 6o + -1ox + 3O + 3xO = 0 + 3O

Reorder the terms:
-3O + 3O + 6o + -1ox + 3xO = 0 + 3O

Combine like terms: -3O + 3O = 0
0 + 6o + -1ox + 3xO = 0 + 3O
6o + -1ox + 3xO = 0 + 3O
Remove the zero:
6o + -1ox + 3xO = 3O

Add '-6o' to each side of the equation.
6o + -1ox + -6o + 3xO = 3O + -6o

Reorder the terms:
6o + -6o + -1ox + 3xO = 3O + -6o

Combine like terms: 6o + -6o = 0
0 + -1ox + 3xO = 3O + -6o
-1ox + 3xO = 3O + -6o

Add 'ox' to each side of the equation.
-1ox + ox + 3xO = 3O + -6o + ox

Combine like terms: -1ox + ox = 0
0 + 3xO = 3O + -6o + ox
3xO = 3O + -6o + ox

Add '-3xO' to each side of the equation.
3xO + -3xO = 3O + -6o + ox + -3xO

Combine like terms: 3xO + -3xO = 0
0 = 3O + -6o + ox + -3xO

Simplifying
0 = 3O + -6o + ox + -3xO

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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