To solve the quadratic equation \( 6x^2 = 22x \) by factoring out the greatest common factor, we first move all terms to one side of the equation:
\[ 6x^2 - 22x = 0 \]
Next, we identify the greatest common factor (GCF) of the terms on the left side. The GCF of \( 6x^2 \) and \( 22x \) is \( 2x \). We factor \( 2x \) out of the equation:
\[ 2x(3x - 11) = 0 \]
Now, we can set each factor equal to zero to solve for \( x \):
- Setting the first factor equal to zero:
\[ 2x = 0 \] \[ x = 0 \]
- Setting the second factor equal to zero:
\[ 3x - 11 = 0 \] \[ 3x = 11 \] \[ x = \frac{11}{3} \]
Thus, the solutions to the equation \( 6x^2 = 22x \) are:
\[ x = 0 \quad \text{and} \quad x = \frac{11}{3} \]
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