# How do you solve x^2-3x = 28 by factoring?

Oct 8, 2015

$x = 7 , - 4$

#### Explanation:

In order to use the zero product principle, we must have a polynomial equal to 0. This means we need to manipulate the equation we have so that it fits this form:

${x}^{2} - 3 x - 28 = 0$

Subtracting the 28 from the right side should fit the form.

Now we can begin factoring. Two numbers that multiply to equal -28 can be -14 and 2, -7 and 4, -28 and 1, and possibly others. But we also need these two numbers to, when added, equal -3. -7 and 4 fit this description. This brings us to the equation:

$\left(x - 7\right) \left(x + 4\right) = 0$

We can then set each part of the factored form equal to 0:

$x - 7 = 0$
$x = 7$
And:
$x + 4 = 0$
$x = - 4$

We then have our answer, $x = - 4 , 7$

I hope this helped!