Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.
Solve a formula when the target variable appears in more than one term
Problem
Given \(A=lw+lh\) with \(w+h\ne~0\), solve for \(l\). Factor the repeated \(l\) from the two terms before dividing by its full coefficient.
Big Picture
What this problem is really about
Since the target variable appears in two terms, dividing immediately would miss part of its coefficient. We’ll factor the repeated variable from both terms, treat the remaining sum as one complete multiplier, and divide by that grouped quantity only after using the given nonzero restriction.
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