Question

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.

Answer 1

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.