start with:
3x^2 = 36 - 3x
subtract 36 and add 3x to both sides of the equation to get:
3x^2 + 3x - 36 = 0
factor out the gcf of 3 to get:
3 * (x^2 + x - 12) = 0
factor (x^2 + x - 12) to get:
3 * (x + 4) * (x - 3) = 0
divide both sides of this equation by 3 to get:
(x + 4) * (x = 3) = 0
set each of these factors 0 to get:
x + 4 = 0
x - 3 = 0
solve for x to get:
x = -4 or x = 3
those are your solutions.
now we'll factor the equation using the quadratic formula.
the quadratic formula is:
(-b) +/- sqrt(b^2-4ac)
x = ------------------------
2a
you set the equation to standard form like we did above to get:
3x^2 + 3x - 36 = 0
you still want to factor out the gcf because that makes the resulting calculations easier.
factor out the gcf to get:
3 * (x^2 + x - 12) = 0
divide both sides of this equation by 3 to get:
x^2 + x - 12 = 0
the equation is now in standard form of:
ax^2 + bx + c, where:
a = 1
b = 1
c = -12
now you are ready to apply the quadratic formula.
replacing a with 1 and b with 1 and c with -12, you will get:
(-1) +/- sqrt((1)^2-4*1*(-12))
x = ------------------------
2*1
simplify this to get:
(-1) +/- sqrt(49)
x = ------------------------
2
simplify further to get:
(-1) +/- 7
x = ------------------------
2
solve for x to get:
x = 6/2 = 3
or:
x = -8/2 = -4
this agrees with what we got above using the factoring method which is good.
those are your solutions.
x = 3 or x = -4