Solving a Formula for the Variable of Interest

A formula like A = h(b1 + b2)/2 looks intimidating because it has five letters in it. The fix is a mindset shift: pick the one letter you want, and freeze every other letter in place as if it were just some number, like 7 or 12. Once you do that, the formula is not a tangled mess anymore. It is an ordinary one-step-at-a-time equation, the same kind you have solved for x a hundred times, just with uglier-looking numbers.

The method is to peel off operations in the reverse order from how they were built up, exactly like undoing PEMDAS backwards. Look at what is being done to your target variable last, and undo that first. For A = h(b1 + b2)/2 solved for b2: the right side is h times a sum, divided by 2. Undo the division by 2 by multiplying both sides by 2, giving 2A = h(b1 + b2). Undo the multiplication by h by dividing both sides by h, giving 2A/h = b1 + b2. Undo the addition of b1 by subtracting it: b2 = 2A/h - b1. For A = P(1+r)^t solved for r: divide both sides by P to get A/P = (1+r)^t, undo the exponent t by taking the t-th root of both sides, then subtract 1 to isolate r.

This skill sits underneath almost every advanced-math question that hands you a formula from geometry, finance, or science and asks for a different variable. It is the same reverse-order unwinding you use to solve any equation, just dressed up with more letters, so the real test is whether you can tell which operation is outermost.