Solve the equation 4x^2-12x=7 algebraically for x.

First subtract 7 from each side of the equation.

4x^2 - 12x - 7 = 0.

Now we can substitute terms into our friend the quadratic equation, which you should memorize. Or we can try a few simple factors. 7 is prime, so to make - 7 one number must be positive and one must be negative.

The first pair I tried, (2x + 1) (2x - 7) yield a middle term of - 12x. Therefore, setting each to zero yields: x = - 1/2, or x = 7/2.