Factoring the ugly quadratic

this kind of quadratic doesn’t have a method or  , (a+b)(a-b).

Ex1. 0.5 -0.4x-1.2

step 1. changed it to another expression to eliminate the fraction and decimals.

5 -4x-12

stept 2. first, we could sure that there are (5x+__)(x+___), through the 5 , because the 5 just has two factors are whole number, 1, 5.

step 3. find out the two number which “+ “to -4, and “times” each other to -12, there are must a number is +, and another -. according to the last term, -12.

the factors (possibility) are, 1, -12;   2, -6;   3,-4; the 2 and-6 is the only pair that sum of -4.

step 4. put the 2, and -6 into the half-complete answer,(5x+_2_)(x+_(-6)_), and verified it to adjust the places of 2 and -6 (it easy for people to put them in the wrong places).

step 5,(5x+_6_)(x+_-2__), adjust the initial answer to get the right place and + or “-” or them. because the 5 influences the whole question, you need to cautious to think about the 5 , because step 3 always just suit the  perfectly.

This is my way to solve those kind of questions, it’s not the fastest but the safest and easiest way for me.