Start with
[tex]P = 2(l+w)[/tex]
Expand the right hand side:
[tex]P = 2l+2w[/tex]
Subtract 2l from both sides:
[tex]P-2l = 2w[/tex]
Divide both sides by 2:
[tex]\dfrac{P-2l}{2}=w[/tex]
And so we solved the equation for the width:
[tex]w = \dfrac{P-2l}{2}[/tex]
