Solve for l A=1/2piw^2+2lw

$A = \frac{1}{2} π w^{2} + 2 l w$

Rewrite the equation as $\frac{1}{2} \cdot (π w^{2}) + 2 l w = A$ .

$\frac{1}{2} \cdot (π w^{2}) + 2 l w = A$

Multiply $\frac{1}{2} (π w^{2})$ .

Combine $π$ and $\frac{1}{2}$ .

$\frac{π}{2} w^{2} + 2 l w = A$

Combine $\frac{π}{2}$ and $w^{2}$ .

$\frac{π w^{2}}{2} + 2 l w = A$

Subtract $\frac{π w^{2}}{2}$ from both sides of the equation.

$2 l w = A - \frac{π w^{2}}{2}$

Divide each term in $2 l w = A - \frac{π w^{2}}{2}$ by $2 w$ and simplify.

Divide each term in $2 l w = A - \frac{π w^{2}}{2}$ by $2 w$ .

$\frac{2 l w}{2 w} = \frac{A}{2 w} + \frac{- \frac{π w^{2}}{2}}{2 w}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 l w}{2 w} = \frac{A}{2 w} + \frac{- \frac{π w^{2}}{2}}{2 w}$

Rewrite the expression.

$\frac{l w}{w} = \frac{A}{2 w} + \frac{- \frac{π w^{2}}{2}}{2 w}$

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{l w}{w} = \frac{A}{2 w} + \frac{- \frac{π w^{2}}{2}}{2 w}$

Divide $l$ by $1$ .

$l = \frac{A}{2 w} + \frac{- \frac{π w^{2}}{2}}{2 w}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$l = \frac{A}{2 w} - \frac{π w^{2}}{2} \cdot \frac{1}{2 w}$

Cancel the common factor of $w$ .

Move the leading negative in $- \frac{π w^{2}}{2}$ into the numerator.

$l = \frac{A}{2 w} + \frac{- π w^{2}}{2} \cdot \frac{1}{2 w}$

Factor $w$ out of $- π w^{2}$ .

$l = \frac{A}{2 w} + \frac{w (- π w)}{2} \cdot \frac{1}{2 w}$

Factor $w$ out of $2 w$ .

$l = \frac{A}{2 w} + \frac{w (- π w)}{2} \cdot \frac{1}{w \cdot 2}$

Cancel the common factor.

$l = \frac{A}{2 w} + \frac{w (- π w)}{2} \cdot \frac{1}{w \cdot 2}$

Rewrite the expression.

$l = \frac{A}{2 w} + \frac{- π w}{2} \cdot \frac{1}{2}$

Multiply $\frac{- π w}{2}$ by $\frac{1}{2}$ .

$l = \frac{A}{2 w} + \frac{- π w}{2 \cdot 2}$

Multiply $2$ by $2$ .

$l = \frac{A}{2 w} + \frac{- π w}{4}$

Move the negative in front of the fraction.

$l = \frac{A}{2 w} - \frac{π w}{4}$