Rearranging Formulas ...?

Question

4 (g-c)/g = g - b(c + 4)

Rearrange the formula so you get a formula in terms of c.
TO FIND C =

Answer 1

4(g - c) / g = g - b(c + 4) : original formula
(4g - 4c) / g = g - bc - 4b : multiply out parentheses
4g - 4c = g^2 - bcg - 4bg : multiply by g to clear denom on right
-4c = g^2 - bcg - 4bg - 4g : subtract 4g from both sides
bcg - 4c = g^2 - 4bg - 4g : add bcg to both sides
c(bg - 4) = g^2 - 4bg - 4g : factor out c on left
c = (g^2 - 4bg - 4g) / (bg - 4) : divide by (bg - 4) to get c alone on left

WHEW !!

Answer 2

rearranging formulas is easy if you use the "change side change sign" method. which is the same as "do the same thing to both sides"

so -
4(g-c)/g = g- b(c+4)
multiply out all the brackets to make life easier -
4g/g - 4c/g = g - bc - 4b (note the -b makes it -4b)
4g/4 = 4 so we are left with
4-4c/g = g - bc - 4b
lets get rid of the g at the bottom, so times everything by g
4g - 4gc/g = g^2 - bcg - 4bg
obviously we cancel out the gs on the left to get
4g - 4c = g^2 - bcg - 4bg
add + bcg to each side to cancel out the one on right
4g - 4c + bcg = g^2 - 4bg
subtract 4g from each side
-4c + bcg (better to write it as bcg - 4c) = g^2 - 4bg - 4g
now we have c one one side and can group like items
c(bg-4) = g^2 -4g(b+1)
divide though by (bg-4) to get c on its own
c = ( g^2 -4g(b+1) ) / (bg-4)

Answer 3

expand the brackets, then collect the terms in c. put these on one side of the equation, and the other terms on the other. then divide the 'other side' by the coefficient of c ( the bit in front of c) and you have a formula for c

Answer 4

4(g-c)/g = g - b(c + 4)
(4g - 4c)/g = g - bc + 4b
4g - 4c = g^2 - bcg + 4bg
-4c = g^2 - bcg + 4bg - 4g
bcg - 4c = g^2 + 4bg - 4g
c(bg - 4) = g^2 + 4bg - 4g
c = (g^2 + 4bg - 4g) / (bg - 4)

Answer 5

4(g - c) = g ² - (gb) (c + 4)
4g - 4c = g² - gbc - 4gb
gbc - 4c = g² - 4gb - 4g
(gb - 4) c = g ( g - 4b - 4)
c = (g) (g - 4b - 4) / (gb - 4)

Answer 6

for what? to establish formula for b,c or g?