Need guidance with rearranging a formula with two brackets and a letter that appears.

Hi MattA147.

The question being begged is: 'How do you solve this problem explicitly for x'.

Changing the subject of a formula basically means that if you have a formula in the form: $y=x+3$ then the 'subject' of the formula is 'y'. Changing the subject to 'x' would yield: $x=y-3$ .

So in your problem we have: $5(x-3)=y(4-3x)$ and we want to make 'x' the subject of the formula.

Let's start by getting rid of those parentheses:

$5(x-3)=y(4-3x)\\ \Rightarrow\\5x-15=4y-3yx$

Now let's solve for 'x':

$5x-15=4y-3yx\\ \Rightarrow\\5x+3yx=15+4y\\ \Rightarrow\\x(5+3y)=15+4y\\ \Rightarrow\\x=\frac{4y+15}{3y+5}$