To solve for the variable #w#, do the same actions on both sides of the equals sign.
In this case, subtract #5.64# from both sides. I'll write out the steps next to the math:
#color(white){color(black)(
(5.64+w=10, qquadqquad "The original problem"),
(w+5.64=10, qquadqquad"Switch around the plus sign"),
(w+5.64color(blue)(-5.64)=10color(blue)(-5.64), qquadqquad"Subtract "5.64" from both sides"),
(wcolor(red)cancel(color(black)(+5.64-5.64))=10-5.64,qquadqquad 5.64-5.64" is just "0),
(w+0=10-5.64, qquadqquad"Rewrite the above step"),
(w=10-5.64,qquadqquad w+0" is just "w),
(w=4.36, qquadqquad10-5.64" evaluates to "4.36)
:}#
That's the answer!