Consider the following quadratic equation:
9x2+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 by factoring, we want to rewrite the equation in the form of (x - a)(x - b) = 0, where a and b are the roots of the equation.
To do this, we first factor out the common factor of 3x:
3x(3x + 7) = 0
Now, we set each factor equal to zero and solve for x:
3x = 0 or 3x + 7 = 0
For the first equation, dividing both sides by 3 gives us:
x = 0
For the second equation, we subtract 7 from both sides:
3x = -7
Dividing both sides by 3 gives us:
x = -7/3
So the solutions to the quadratic equation 9x^2 + 21x = 0 are x = 0 and x = -7/3.