To solve the quadratic equation \( 5x^2 + 75x = 0 \) by factoring out the greatest common factor (GCF), follow these steps:
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Identify the GCF: The GCF of the terms \( 5x^2 \) and \( 75x \) is \( 5x \).
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Factor out the GCF: \[ 5x(x + 15) = 0 \]
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Set each factor equal to zero:
- \( 5x = 0 \)
- \( x + 15 = 0 \)
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Solve each equation:
- For \( 5x = 0 \): \[ x = 0 \]
- For \( x + 15 = 0 \): \[ x = -15 \]
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Write the solutions: The solutions to the equation \( 5x^2 + 75x = 0 \) are: \[ x = 0 \quad \text{and} \quad x = -15 \]
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