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

Answer

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Answer

The solutions to the equation are $y = \boxed{-\frac{7}{5}}$ and $y = \boxed{\frac{7}{5}}$.

Steps

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 $y = \boxed{\frac{7}{5}}$.