here we're asked to solve a quadratic
that's already equal to zero but notice
we have fractional coefficients whenever
you have an equation you can always
clear the fractions by simply
multiplying both sides of the equation
by the LCD okay in this case if we
multiply both sides by 12 we should be
able to clear the fractions on the right
side zero times twelve is just zero but
here when I distribute the twelve twelve
times one half is 6x squared
twelve times negative 1/12 is minus 1x
and then twelve times negative one-sixth
is minus two
okay so by multiplying both sides by the
LCD notice no more fractions again be
careful that only works for equations
now it's going to be much easier to
factor the resulting trinomial okay so
here we have to put some thought into
the coefficients six we'll be able to
break up as one times six or two times
three and two looks like there's only
one choice one times two we want our
middle term to be negative 1x so you
know it looks like we should use two and
three one and two because that will give
us a four and A three four and three in
some weird way adds up to one okay so
after putting a little bit of thought
into those coefficients let's break up
6x squared as 2x times 3x now we know
we're after all ready so let's put let's
break up two but put the two over here
and the one there okay so that gives me
a 4x and a 3x 4x and 3x adds up to
negative 1x if the four is negative and
the three is positive okay so the middle
term will be negative 1x but how about
the N term positive 1 times negative 2
is negative 2 so it looks good be sure
to spend some time on the factoring step
that's where most folks make errors once
you have it factored correctly then set
each factor equal to zero you're almost
home-free
okay so 3x minus 2 equals zero and then
solve each one of these linear
pertly so 2 x equals negative 1 x equals
negative 1/2
okay so 3 X adding 2 to both sides
equals 2x equals dividing by 3 2/3 okay
so my solutions here are negative 1/2
and 2/3 okay so what you can do here
when you have fractional coefficients is
multiply both sides by the LCD and then
you'll have integer coefficients solve
like normal it's much easier to factor
polynomials with integer coefficients
then fractional coefficients
