Factor 2x^2-50+12xy+60y

$2 x^{2} - 50 + 12 x y + 60 y$

Factor $2$ out of $2 x^{2} - 50 + 12 x y + 60 y$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 50 + 12 x y + 60 y$

Factor $2$ out of $- 50$ .

$2 x^{2} + 2 \cdot - 25 + 12 x y + 60 y$

Factor $2$ out of $12 x y$ .

$2 x^{2} + 2 \cdot - 25 + 2 (6 x y) + 60 y$

Factor $2$ out of $60 y$ .

$2 x^{2} + 2 \cdot - 25 + 2 (6 x y) + 2 (30 y)$

Factor $2$ out of $2 x^{2} + 2 \cdot - 25$ .

$2 (x^{2} - 25) + 2 (6 x y) + 2 (30 y)$

Factor $2$ out of $2 (x^{2} - 25) + 2 (6 x y)$ .

$2 (x^{2} - 25 + 6 x y) + 2 (30 y)$

Factor $2$ out of $2 (x^{2} - 25 + 6 x y) + 2 (30 y)$ .

$2 (x^{2} - 25 + 6 x y + 30 y)$

Rewrite $25$ as $5^{2}$ .

$2 (x^{2} - 5^{2} + 6 x y + 30 y)$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$2 ((x + 5) (x - 5) + 6 x y + 30 y)$

Factor $6 y$ out of $6 x y + 30 y$ .

Factor $6 y$ out of $6 x y$ .

$2 ((x + 5) (x - 5) + 6 y (x) + 30 y)$

Factor $6 y$ out of $30 y$ .

$2 ((x + 5) (x - 5) + 6 y (x) + 6 y (5))$

Factor $6 y$ out of $6 y (x) + 6 y (5)$ .

$2 ((x + 5) (x - 5) + 6 y (x + 5))$

Factor.

Factor $x + 5$ out of $(x + 5) (x - 5) + 6 y (x + 5)$ .

Factor $x + 5$ out of $6 y (x + 5)$ .

$2 ((x + 5) (x - 5) + (x + 5) (6 y))$

Factor $x + 5$ out of $(x + 5) (x - 5) + (x + 5) (6 y)$ .

$2 ((x + 5) (x - 5 + 6 y))$

Remove unnecessary parentheses.

$2 (x + 5) (x - 5 + 6 y)$