12x^2+10x-12 factor show work please?

First take 2 out as it is common in all terms, so the given expression becomes:

2(6x^2 +5x -6)

Now multiply the coeffiicient of x^2 with the last term(-6) and get two factors so that their sum gives the middle term coefficient: these will be 9,-4. Wrtie the above expression in terms of factors:

2{6x^2 -9x +4x -6}

Now group the terms and take common:

2{3x(2x-3) +2(2x-3)}

or 2(2x-3)(3x+2) is the factorization of your expression.

Take a factor of 2 out to make it easier first:

12x^2+10x-12 = 2(6x^2 + 5x - 6)

Then find the factors which work for the polynomial 6x^2 + 5x - 6.

This takes a bit of trial and error, but you should end up with:

2(3x - 2)(2x + 3).

Hope this helps.

Root of the equation ax^2 + bx + c = 0

Here a=12

b=10

c=-12

Applying Quadratic Formula

x=(-b±√(b^2-4ac))/2a

x=(-10±√(10^2-4(12)(-12)))/2(12)

x=-1.5 and-0.666667