If $(w+13)^2=(3w+7)(2w+4)$, find $w^2$. Express your answer as a decimal.
I notice that the equation has a squared term on the left and a product of two binomials on the right. I wonder if I can simplify the equation by expanding the left side and using the distributive property on the right side. I get $w^2+26w+169=6w^2+26w+28$. I see that I can subtract $26w$ from both sides and get $w^2+169=6w^2+28$. I want to isolate $w^2$ on one side, so I subtract $w^2$ from both sides and get $169=5w^2+28$. I subtract $28$ from both sides and get $141=5w^2$. I divide both sides by $5$ and get $28.2=w^2$. This is the value of $w^2$ I need to find.

