Question 389646
Recall the general form for a quadratic equation: 

ax^2 + bx + c


-2x^2 + 13x - 21


We will use the Decomposition Method for factoring.

First, multiply a*c = (-2)(-21) = 42


So you need to find two numbers that multiply to 42 and add up to the b term, +13. This is pretty easy: the numbers are 7 and 6.


Now the hard part is to decompose the b term, +13, into these two factors. Notice that I list 6x first, so that it pairs with the 2x^2, and the 7x second, so that it pairs with the 21 at the end. 


-2x^2 + 13x - 21
-2x^2 + 6x + 7x - 21


Next, factor out the -2x and 7 from each. Note that you are left with identical terms, (x-3) for each.


-2x(x-3) + 7(x-3)


Combine the -2x and 7 into one bracket:


(-2x + 7)(x-3)

This leaves you with two answers, which you can find by setting each bracket to zero, and solving for x:

-2x+7 =0
7=2x
x=7/2


x-3=0
x=3


Hope this helps! Let me know if you're confused by anything.