Volume Equation - no idea how to solve it

So, I have:

"A large plywood box has a volume of 768 ft^3. Its length is 16 ft greater than its height, and its width is 4 ft less than its height. What are the dimensions of the box?"

This is how I have set up the equation:

(h+16)(h-4)(h)=768

Is this correct? If so, I can't figure out how to solve it. HELP!

I got
(h+16)(h-4)(h)=768
as well

and
h^3+12h^2-64h=768

which grouped to
h^2(h+12)-64(h+12)
(h^2-64)(h+12)

h=+/-8,-12
but you cannot have negatives for the real world
h=8

h^3+12h^2-64h=768
8^3+12(8^2)-64(8)=768
512+768-512=768

768/8=96

L*W=96
(8+16)(8-4)=96
24*4=96
yes it does

the box is 8 by 24 by 4

[I had to do it twice]

Multiply out the equation:
h^3+12h^2-64h=768
Move the 768 over:
h^3+12h^2-64h-768=0
this factorises to:
(h-8)(h+8)(h+12)=0
therefore h=8,-8,-12.
however we don't want a negative length, so h=8

dimension would be height:8, length:24, width:4

yes the equation is absolutely correct. then you have to solve for 'h'


(h+16)(h-4)(h) = 768

(h^2 - 4h + 16h - 64)h = 768

(h^2 + 12h - 64)h = 768

(h^2 + 12h + 6^2 - 6^2 - 64)h = 768

{(h + 6)^2 - 36 - 64}h = 768

h(h + 6)^2 - 100h = 768

(h+16)(h-4)(h) = 768
h³ + 12h² - 64h = 768
h³ + 12h² - 64h - 768 = 0
Factor by Grouping:
h(h² - 64) + 12(h² - 64) = 0
(h + 12)(h² - 64) = 0
(h + 12)(h + 8)(h - 8) = 0
h = 8 (-8, -12)
h+12 = 20
h-4 = 4

Dimensions: 20 x 8 x 4

correct so far.

then expand out to give:

(h^3) + 12(h^2) - 64h = 768

then work out h.

you should then get h = 8 or -8 or -12 and we select the positive answer which is h=8

H+16=L
W=H-4
L*W*H = 768
substitute

Height is 8 length is 24 and width is 4

Yes, it is correct.