Write the polynomial: x^2 - 4x + 6x - 24 = 0. Simplify the expression: x^2 + 2x - 24 = 0.
Make a factor table. Draw a horizontal line. Draw a vertical line intersecting the middle of the horizontal line. Write the constant, which is 24 in this example, on the horizontal line. List pairs of factors of the constant and write each number on either side of the vertical line. For example, the pair factors of 24 are: 1 x 12, 2 x 24, 3 x 8 and 4 x 6.
Choose the factor pair whose sum or difference is equal to the number in front of the single x variable, which is 2 in the example. So choose 4 and 6.
Write two open parenthesis in the following way: (x + _ ) (x - _ ). Substitute 4 and 6 in the second parts of the expressions: (x + 4) (x - 6).
Multiply the expressions into a polynomial, using the "FOIL" method, which means "First, Outside, Inside, Last": x^2 - 6x + 4x - 24 = x^2 - 2x - 24. This is not the same expression as x^2 + 2x - 24.
Switch the placement of 4 and 6 in the set of parenthesis: (x + 6) (x - 4). Multiply using FOIL: x^2 + 2x - 24. This expression is equal to the original expression.
Set the individual expressions of the equation equal to zero and solve: (x + 6) = 0 and (x - 4) = 0; x = -6 and 4.