# Solve by Factoring 25^(x^2)*5^(3x)=25 Move to the left side of the equation by subtracting it from both sides.
Multiply .
Rewrite as .
Apply the power rule and multiply exponents, .
Use the power rule to combine exponents.
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.
Solve for .
Move to the left side of the equation by subtracting it from both sides.
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
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.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
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