Consider the following quadratic equation:
12x^2=−9x
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 it in the form of ax^2 + bx + c = 0. In this case, the equation is already in that form, so we can proceed with factoring.
First, let's rewrite the equation with all terms on one side:
12x^2 + 9x = 0
Next, we factor out the greatest common factor, which is 3x since both terms have it:
3x(4x + 3) = 0
Now we can set each factor equal to zero and solve for x separately:
3x = 0 or 4x + 3 = 0
For the first equation, divide both sides by 3 to solve for x:
x = 0/3
x = 0
For the second equation, subtract 3 from both sides and solve for x:
4x = -3
x = -3/4
So the solutions to the quadratic equation 12x^2 = -9x are x = 0 and x = -3/4.