Ensure the equation is written out in standard form. Write out two sets of parentheses with the x's to the left and question marks or spaces to the right: (x +/- ?)(x +/- ?) = 0
List all the pairs of numbers that multiply to give "c," the end number.
Search through the list and find a pair of numbers that add or subtract to give the value of "b." For example, in the equation x^2 + 7x + 12, the multiplication pairs would be 1 x 12, 2 x 6 and 3 x 4. Of these the last pair of numbers, 3 x 4, add together to give 7.
Replace the question marks in the parentheses with the numbers using the appropriate + or - signs. Check your answer is correct by expanding the parentheses out again so that they return you to the original equation.
Rearrange the equation into the standard format. For example, 3x^2 + 7x = 6 would be rearranged to form 3x^2 + 7x - 6 = 0.
Write out two sets of parentheses with the x's inside and to the left. Enter the value of "a" into the left hand parentheses in front of the x. For example, (3x +/- ?)(x +/- ?) = 0.
List all the pairs of numbers that multiply with one another to give the value of "c." In this example, those pairs would be 1 x 6 and 2 x 3.
Write out all the possible combinations of numbers which, when placed inside the parentheses, multiply and then add or subtract to give the value of "b." Remember that each pair of numbers can be tried in two different positions. For example (3x 3)(x 2) multiplies to give 6x and 3x and adds or subtracts to give 9x or 3x. In the alternative position (3x 2) (x 3) multiplies to give 9x and 2x, which adds or subtracts to give 11x or 7x, the latter being the value of "b."
Enter the numbers into the parentheses and fill in the correct + or - signs. Double-check your answer is correct by expanding the parentheses so that they return you to the original equation.