To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms in the equation.
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \). Thus, we can factor \( 2x \) out of the equation:
\[ 2x(x - 7) = 0 \]
Next, we set each factor equal to zero:
- \( 2x = 0 \)
- \( x - 7 = 0 \)
From the first equation:
\[ 2x = 0 \implies x = 0 \]
From the second equation:
\[ x - 7 = 0 \implies x = 7 \]
Thus, the solutions to the equation \( 2x^2 - 14x = 0 \) are:
\[ \boxed{0} \quad \text{and} \quad \boxed{7} \]