If x^2-5x+6=0, solve for x.

Since x^2-5x+6=0 is a quadratic we need to factorize before solvingAll quadratics fall under this formula ax^2+bx+c=0 so in this case a=1, b=-5 and c=6Drawing the very common ac b table we get: ac|b 6 |-5So we ask ourselves, what two numbers multiply to give 6 but add to give -5? With little thought the answer is -2 and -3So: x^2-5x+6=0 x^2-2x-3x+6=0 Now factorize the left two terms and the right two terms of the left hand sidex(x-2)-3(x-2)=0 Now factorize the left hand side entirely(x-3)(x-2)=0In order for a product of two numbers to equal zero, at least one of them must be zero.Therefore x-3=0 or x-2=0Therefore x=3 or x=2