FOIL method worked in reverse??

[kristenbarchus]

I hope that I have the right catagory - we have a word problem that we need help with.

"In a certain rectangle, the length is 2 centimeters more than 3 times the width. The area is 120 square centimeters. Find the dimensions."

The following steps are the steps that have been provided, but at the signified step, we cannot tell how the next line was achieved. I beleive it was a reverse of the FOIL method, but I do not understand how to actually work the reverse of FOIL.

A = lw

(120 cm^2) = (3w + 2cm)(w)
120 cm^2 = 3w^2 + 2cmw
-3w^2 - 2 cmw + 120 cm^2 = 0
-1 (-3w^2 - 2 cmw + 120 cm^2) = -1(0)
3w^2 + 2 cmw - 120 cm^2 = 0

(Here is where it appears that the method FOIL was operated in reverse, but I cannot understand how to do that)

(3w + 20cm)(w - 6cm) = 0

The rest of the example steps seem too jumbled to understand as well, but answers are shown as follows:

w = 6cm
l = 20 cm

Please help! My 13 year old is ready to throw her book through the computer screen!

Thank you!

 

[Denis]

It is this simple:

Let w = width ; then length = 3w + 2
since area = 120, then :
w(3w + 2) = 120
3w^2 + 2w - 120 = 0
(3w + 20)(w - 6) = 0
w = -20/3 or w = 6 : only w = 6 is possible

so width = 6 and length = 3(6) + 2 = 20

Clear?