Write out the equation and set it equal to zero. For instance, you might have: f(x) = x^3 + 4x^2 - 5x - 20. To set it equal to zero, simply add an equal symbol and the number zero on the right side: f(x) = x^3 + 4x^2 - 5x - 20 = 0.
Group terms within the equation that appear to have like terms that can be factored. Drop the f(x) from the equation because it is merely a reminder that this is an algebraic function. Since the first two terms in this example have "x" raised to a power, you would group them together. You also would group the last two terms together because 5 and 20 are both divisible by 5. The grouped equation in this example would be: (x^3 + 4x^2) + (-5x - 20) = 0.
Factor out terms that are common to the grouped portions of the equation. In this example, the x^2 is common to both terms in the first set of parentheses. Therefore, you would write: x^2 (x + 4). The number -5 is common to both terms in the second grouping, so you would write -5 (x + 4). The entire equation at this point would look like this: x^2 (x + 4) - 5 (x + 4) = 0.
Combine the two terms from the outside of each parentheses into their own set of parentheses, and add the terms within the previous parentheses once. In this example, you would write (x^2 - 5) (x + 4) = 0.
Set each polynomial within a set of parentheses equal to zero. In this example, you would write: x^2 - 5 = 0, and x + 4 = 0.
Solve both expressions. Remember to change the sign of a number that you move across the equal sign. In this case, you would write x^2 = 5. Then you would take the square root of both sides to get x = +/- 2.236. This accounts for two of the zeros for the function: +2.236 and - 2.236. Then you would move the 4 to the other side of the equation for the second part and change its sign so that you would have: x = -4. This is the third zero of the equation.