Arectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. what are the dimensions of the rectangle?

length =
width =

Area=legnth times width
A=LW

width=7 less than legnth
W=L-7
sub L-7 for W

A=330=L(L-7)
330=L^2-7L
minus 330 both sides
0=L^2-7L-330
factor
find what 2 numbers multiply to get -330 and add to get -7
-22 and 15
0=(L-22)(L+15)
set to zero
L-22=0
L=22
L+15=0
L=-15, false, not negative legnths

L=22
sub
L-7=W
22-7=15

Legnth=22 cm
Width=15 cm