# Solve for x 3^(2x)-108*3^x+2187=0

Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Replace the left side with the factored expression.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Create equivalent expressions in the equation that all have equal bases.
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Create equivalent expressions in the equation that all have equal bases.
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
The final solution is all the values that make true.
Solve for x 3^(2x)-108*3^x+2187=0