A quadratic equation is written in the form: ax^2 + bx + c. To solve a quadratic equation by the long method, write down the equation, for example: x^2 + 8x + 12. Assign the values of the variables, in this case, a = 1, b = 8 and c = 12.
Multiply a times c: in this case a = 1 and c = 12 so ac = 12. Remember to write down the sign if the product is a negative number. Write down the value of b with the sign:
b = +8
Figure out all the pairs of numbers whose products equal the value of ac. Since ac in this example equals 12, the pairs would be: (6 and 2), (3 and 4) and (12 and 1). Now find the pair that adds up to the value of b. Here 6 and 2 add up to the value of b which is 8.
Write out the expanded equation, replacing bx in the original equation with the pair just selected: (x^2 + 8x + 12) -> (x^2 + 6x + 2x + 12). Look at this new equation and factor out common elements. This equation can be factored to: x(x +6) + 2(x + 6). It can be further factored by taking the common element (x + 6) out, yielding the factored expression: (x + 6)(x + 2).