Please factor this trinomial: 12x²-18x-21

To factor the trinomial, we'll consider the
equation:

12x^2 - 18x - 21 = 0

We'll
divide by 3 the trinomial:

4x^2 - 6x - 7 =
0

To write the quadratic as a product of linear factors, we'll have
to determine the roots of the quadratic.

We'll apply the quadratic
formula:

x1= [-b+sqrt(b^2 -
4ac)]/2a

a,b,c, are the coefficients of the
quadratic:

x1 = [6+sqrt(36 + 112)]/8

x1
= (6+sqrt148)/8

x1 = (6+2sqrt37)/8

x1 =
(3+sqrt37)/4

x2 = (3-sqrt37)/4

We'll
write the quadratic as a product of linear
factors:

12x^2 - 18x - 21 =
3([x-(3+sqrt37)/4]*[x-(3-sqrt37)/4]