Make x the subject of the formula: y = 3x – 9c/4x + 5d

Start with y = (3x − 9c)/(4x + 5d). To get rid of the fraction, multiply both sides by the denominator (4x + 5d): y(4x + 5d) = 3x − 9c, which opens out to 4xy + 5dy = 3x − 9c.

Now gather every term containing x on one side and everything else on the other. Take 3x to the left and 5dy to the right: 4xy − 3x = −9c − 5dy.

Factor out x on the left: x(4y − 3) = −9c − 5dy. The right side can be written more neatly by taking out the minus sign: −9c − 5dy = −(9c + 5dy).

Finally divide both sides by (4y − 3): x = −(9c + 5dy)/(4y − 3). That is x made the subject. Note the sign care needed — both 9c and 5dy end up negative, so the minus must apply to the whole bracket, not just one term.