Consider the following quadratic equation:
6x^2+21x=0
Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the quadratic equation 6x^2 + 21x = 0 by factoring, we can start by factoring out the greatest common factor (GCF), which is 3x:
3x(2x + 7) = 0
Now, we can set each factor equal to zero to find the values of x:
3x = 0 or 2x + 7 = 0
From the first equation, when 3x = 0, we can divide both sides by 3 to isolate x:
x = 0/3
x = 0
From the second equation, when 2x + 7 = 0, we can subtract 7 from both sides:
2x = -7
Finally, we can divide both sides by 2 to isolate x:
x = -7/2
Therefore, the solutions to the quadratic equation 6x^2 + 21x = 0 are x = 0 and x = -7/2.