y * y = y^2, therefore your equation becomes y^2 - y = 6
subtract 6 from both sides of the equation to get y^2 - y - 6 = 0
you now have a quadratic equation in standard form that you can factor to get the possible solutions.
the factors of this equation become (y - 3) * (y + 2) = 0
if you multiply those 2 factors together, you will get the original equation of y^2 - y - 6 = 0
set each of the factors equal to 0 and solve for y.
you will get y = 3 or y = -2.
those are the values of y that will make the equation of y^2 - y - 6 = 0 true.
normally you work with x as the variable name.
in this case they used y.
most of the formula assume that the variable name is x.
this can cause some confusion unless you understand what's going on and can translate the variable used to the standard variable name of x.
an example would be the equation that you used.
your equation is y^2 - y - 6 = 0
the quadratic formula assumes you are using the variable x, rather than any other variable name.
the quadratic formula is x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a).
the quadratic formula assumes your equation is in the form of ax^2 + bx + c = 0
to use the quadratic formula on your equation, you need to understand that x and y are just variable names and can be used interchangeably.
if you let x equal y, then your equation of y^2 - y - 6 = 0 becomes x^2 - x - 6 = 0
now you can use the quadratic formula.
you will get stuff like this fairly often and so it becomes necessary for you to be able to translate variable names to the standard ones used in the formulas that normally assume standard variable names.
suppose you wanted to graph the equation of z = y^2 - y - 6.
most graphing software assume the independent variable is x and the dependent variable is y.
you would need to set z = y and y = x to get y = x^2 - x - 6.
now you can graph it using most graphing software.
if you have any further questions regarding what is y, just let me know.
factoring is another story.
you should be able to factor by now, but if not, here's a decent reference.
