Question

How do you solve `6x^2 + 5x - 4 = 0` by factoring?

Answer 1

The solutions are
`color(blue)(x=-4/3`

`color(blue)(x=1/2`

Explanation:

`6x^2+5x−4=0`

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 6*-4 = -24`
and
`N_1 +N_2 = b = 5`

After trying out a few numbers we get `N_1 = 8` and `N_2 =-3`
`8*-3 = -24`, and `8+(-3)= 5`

`6x^2+5x−4=6x^2-3x+8x−4`

`=3x(2x-1) +4(2x-1)=0`

`=(3x+4)(2x-1) =0`

Now we equate the factors to zero.
`=3x+4 =0, color(blue)(x=-4/3`

`=2x-1 =0, color(blue)(x=1/2`