The zeros of the function means the value of x which makes f(x) is equal to zero.
f(x) = 0
x² + 15x + 56 = 0
I break 15x into 8x and 7x
x² + 8x + 7x + 56 = 0
(x² + 8x) + (7x + 56) = 0
Do factorization of the terms inside the parenthesis
x² and 8x have the same factor, that is x. Separate x by the parenthesis.
x(x + 8) + (7x + 56) = 0
7x and 56 have the same factor, that is 7. Separate 7 by the parenthesis
x(x + 8) + 7(x + 8) = 0
There are two same factors of (x + 8), separate (x + 8) by the parenthesis
(x + 8)(x + 7) = 0
(x + 8) multiplied by (x + 7) is equal to zero. What make the zero of function is when x + 8 = 0 or when x + 7 = 0
x + 8 = 0
x = -8
x + 7 = 0
x = -7
The zeros of the function is -8 and -7