How to reverse an equation

How can I reverse this equation as I am trying to find the value of z if is x is known

at the moment the equation works out the value of x and is as follows:

x = a + (z - d) * (b - a)/ (c - d)

now I know the value of x, I can populate the rest of the values but now i want to work out a new value of x but this leads me to not know what the change in value of z is, so how do I reverse the equation to find this out??

x = is known
a = is known
b = is known
c = is known
d = is known

z = this is the value I need to work out

can anyone help or is this never going to work??

abeintot ;)

It's hard to tell if you mean

x = a + [(z - d) * (b - a)/ (c - d)]

or

x = [a + (z - d) * (b - a)]/ (c - d)

I'm going to assume the first one, since that's what the equation you've written works out to.

Work it step by step

x - a = (z - d) * (b - a)/ (c - d)
(x - a) * (c - d) = (z - d) * (b - a)
[(x - a) * (c - d)] / (b - a) = z - d
d + {[(x - a) * (c - d)] / (b - a)} = z

You mean rearrange the following in terms of “z”
x = a + (z - d) * (b - a)/ (c - d)
HOWEVER – there is some confusion
Look at HOW its been written.
Do you mean x = [ a + (z - d) * (b - a) ] / (c - d)
OR x = a + (z - d) * [ (b - a)/ (c - d) ]
In the future use brackets more to “package-up” the variables since how it is written is open to some confusion.