Graph the quadratic. The points where the graphed curve crosses the X axis are roots of the quadratic. If the curve crosses the X axis at r, then r is a root of the quadratic and X - r is a factor of the quadratic. If the curve does not cross the X axis, then the roots are both complex and the quadratic does not have solutions that are usable for a practical application.
Find the candidate factors by looking at the first and last numbers in the quadratic. For example, if the quadratic is 2X^2 - 4X - 6 = 0, the first and last numbers are 2 and 6, so the possible factors will have first numbers 1 or 2 and last number 1, 2, 3 or 6. The candidates are X - 1, X + 1, X - 2, X + 2, X - 3, X + 3, X - 6, X + 6, 2X - 1, 2X + 1, 2X - 2, 2X + 2, 2X - 3, 2X + 3, 2X - 6 and 2X + 6.
Try all of the candidates to find the factors. For 2X^2 - 4X - 6 = 0, the candidates that divide the quadratic polynomial leaving a remainder are 2X - 2 and X - 3. This means that 2X^2 - 4X - 6 = (2X + 2)(X - 3), or (2X + 2)(X - 3) = 0. If 2X + 2 = 0 then X = -1. If X - 3 = 0 then X = 3. Therefore X = -1 and X = 3 are solutions for 2X^2 - 4X - 6 = 0.