Can you help me with algebra HW?!?!?!?!?

Question

Originally, a rectangle was three times as long as it was wide. When 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an area of 90 cm^2. Find the dimensions of the new rectangle.

I need to use factoring to solve this....

Answer 1

Let the original  width be w.

Then the original length was 3w.

After modification, the width was w + 5, and the length 3w - 2.

The area of the new rectangle was (w + 5)(3w - 2).

Therefore:

(w + 5)(3w - 2) = 90

3w^2 + 13w - 100 = 0

(3w + 25)(w - 4) = 0

w = 4 or - 25 / 3.

Discarding the negative result, the new width was w + 5 = 9 cm, and the new length 3w - 2 = 10 cm.