To solve the quadratic equation \( 12x^2 + 20x = 0 \) by factoring out the greatest common factor (GCF), we can first identify the GCF of the coefficients.
The GCF of 12 and 20 is 4. Therefore, we can factor out \( 4x \) from the equation:
\[ 12x^2 + 20x = 4x(3x + 5) = 0 \]
Now, we set each factor equal to zero:
- \( 4x = 0 \)
- \( 3x + 5 = 0 \)
For the first equation:
\[ 4x = 0 \implies x = 0 \]
For the second equation:
\[ 3x + 5 = 0 \implies 3x = -5 \implies x = -\frac{5}{3} \]
Thus, the solutions to the quadratic equation \( 12x^2 + 20x = 0 \) are:
\[ x = 0 \quad \text{and} \quad x = -\frac{5}{3} \]
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