Solve the equation for the variable y: $25 y^{2}-49$

Step 1 ：The given equation is a difference of squares, which can be factored as \((5y)^2 - (7)^2\).

Step 2 ：The difference of squares can be factored as \((a-b)(a+b)\), where \(a = 5y\) and \(b = 7\).

Step 3 ：After factoring, we can solve for \(y\) by setting each factor equal to zero.

Step 4 ：The solutions to the equation are \(y = \boxed{-\frac{7}{5}}\) and \(y = \boxed{\frac{7}{5}}\).