Solve 2x^2-14x+12=0

Firstly, we can divide through by 2 to get a simpler form of the equation: x^2-7x+6=0. To solve this quadratic equation we need to factorise it. We do this by splitting it up into two brackets which would multiply out to give the expression x^2-7x+6. To factorise this we need two numbers that multiply to give +6 and add to give -7. So we write out the factors of 6 and identify the pair that satisfies our criteria. Factors of 6 are 6 and 1, 3 and 2, -6 and -1 and -3 and -2. The factors we need are -6 and -1 because they multiply to give 6 and add to give -7. So the factorised equation is (x-6)(x-1)=0.Now, each of these brackets would be a number once x is assigned a value so we practically have two numbers being multiplied to give 0. If either one of the two numbers was 0 then their product would be 0 so the equation would be satisfied hence why we set each of the brackets to 0. So if (x-6)=0 then x=6 and if (x-1)=0 then x=1. Both of these are solutions to the equation. In scenarios where x=1 or x=6, the equation would be satisfied.