Solve x^2-6x+8=0

To solve this equation we must first factorise it. To do this we initially write two brackets containing x equal to zero like this (x )(x )=0.Then we want to identify the other part of our bracket. These two numbers must multiply to give 8 and add to give -6.possible multiplications are 1x8 and 2x4 as well as their negative equivalents (-1)x(-8) & (-2)x(-4).By looking at these pairs of numbers we can see the only numbers that add to give -6 are -2 & -4.so these are the numbers in our brackets, giving us a factorised equation (x-2)(x-4)=0 .now that we have simplified our equation to a factorised form, we must be aware that zero multiplied by any number is always equal to zero. this means that if either of the brackets are equal to zero our equation will be satisfied.This gives x-2=0 or x-4=0 which we can see are true when x = 2 or x=4 and so these are the solutions to our equation.