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.
- Combine the like terms: \[ 5x + 75x = (5 + 75)x = 80x \]
So, we can rewrite the equation as: \[ 80x = 0 \]
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Now, we can factor out the GCF, which is \( 80 \): \[ 80x = 0 \]
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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: \[ \boxed{0} \]
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