Solve the equation: x^2 +8x + 12 = 0

This is a classic GCSE-style equation :)
1) Always write out the original equation for clarity (and so that you don't have to look back at the question constantly) :)x^2 + 8x + 12 = 02) Notice that this is quadratic equation and is of the form ax^2 + bx + c (remember the examiner can write the equation using any letter (instead of just x) but this would be just to confuse you (as we all know examiners like to do :D) and the constants a, b and c are just numbers (or coefficients if you want to be fancy :p)), so continue as follows:i) Find 2 numbers such that if you add them together they make b (8 in this case), and if you multiply them together you would get a*c (12 in this case, i.e. 1 x 12). The nice thing about this is that it keeps your timestables skills (for lack of a better word :D) sharp as well. Answer: 6 and 2 :)ii) split the 'bx' part out into the answers above as shown (you will notice that it's the same equation as before since you can combine 6x + 2x into 8x. You'll also be able to see the wisdom behind that in a sec :) ):x^2 + 6x + 2x + 12 = 0iii) factor out as shown:x (x + 6) + 2(x + 6) = 0iv) Notice that the contents of the two brackets are the same. Remember, they will always be the same (for this form of equation. The answer now lies in just taking the contents of one of the closed brackets as one solution to the equation and everything outside the brackets can be combined into another bracket. This might sound confusing tbh but is best explained face-to-face on a whiteboard. It's really very simple:(x + 2) (x + 6) = 0v) Finally, just handle each bracket separately as shown:x + 2 = 0x = -2--------x + 6 = 0x = -63) Hence, the solution to this question is:x = -2, - 6This the step-by-step process to solve any quadratic equation of the form ax^2 + bx + c = 0 (even if things are rearranged). That's the beauty of Math. Everything is logical and follows patterns that anyway can learn to understand AND master (with just a bit of practice):)