I am in 7th grade and getting ready to take the SAT in January I am confused with the terms you are using in the solution can someone explain it to me in simpler terms.

Nicole, I guess the issue is the minus sign before the factor.

Given:
(x-2)(x+4) - (x-3)(x-1) = 0
Each braces is a factor, another way to write it is:
1(x-2) * 1(x+4) - 1(x-3) * 1(x-1) = 0
As you can see before the third factor it states -1
Multiplying this third factor with -1 gives us 1(-x+3) so we'll get:
1(x-2) * 1(x+4) + 1(-x+3) * 1(x-1) = 0
Without the obvious times 1 and the multiplication sign, we'll get:
(x-2)(x+4) + (-x+3)(x-1) = 0
The first set factors multiplied give product (x^2 +4x -2x -8) combine like terms to (x^2 +2x -8) so we'll get:
(x^2 +2x -8) + (-x+3)(x-1) = 0
The 2nd set of factors multiplied give product (-x^2 +1x +3x -3) combine like terms (-x^2 +4x -3) so we'll get:
(x^2 +2x -8) + (-x^2 +4x -3) = 0
Now we can get rid of the parentheses/braces and we'll get:
x^2 +2x -8 -x^2 +4x -3 = 0
A more ordered rewrite (but still equal): x^2 -x^2 +2x +4x -8 -3 = 0
Now we combine like terms and get:
6x - 11 = 0
Add +11 to both sides:
6x = 11
Divide both sides by 6:
x = 11 / 6 and that's our answer.

Niels

Greetings from Holland

Ps.
After getting it, you will go this way:
(x-2)(x+4) - (x-3)(x-1) = 0
(x^2 +2x -8) - (x^2 -4x +3) = 0
Now we multiply the 2nd factor with negative 1
(x^2 +2x -8) + (-x^2 +4x -3) = 0
Get rid of parentheses:
x^2 +2x -8 -x^2 +4x -3 = 0
Combine like terms:
6x - 11 = 0
Add +11 to both sides:
6x = 11
Divide both sides by 6:
x = 11 / 6 and that's our answer