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To solve the equation \( 5x + 75x = 0 \) by factoring out the greatest common factor (GCF), we first need to combine the terms on the left-hand side.
1. Combine the like terms:
\[
5x + 75x = (5 + 75)x = 80x
\]
So, we can rewrite the equation as:
\[
80x = 0
\]
2. Now, we can factor out the GCF, which is \( 80 \):
\[
80x = 0
\]
3. To solve for \( x \), we set the equation to zero and divide by \( 80 \):
\[
x = 0
\]
Thus, the solution to the equation \( 5x + 75x = 0 \) is:
\[
\boxed{0}
\]