To factor a quadratic equation that has a leading coefficient, multiply the most and least significant coefficients together. In this case 6 * -4 = -24
We need to find two numbers that multiply to -24 and add to -5. We will split the middle term into these two numbers.
6x^2 -8x + 3x - 4 = 0
Here you can see that we split -5x into -8x and 3x.
Now we can factor by grouping. To do this, group the first two terms together and the last two terms together. Factor out whatever you can.
(6x^2 - 8x) + (3x - 4)
2x(3x - 4) + 1(3x - 4)
Notice that the second group had nothing to factor out so we just pull out a 1. Now we can rearrange the factored form according to the distributive property.
(2x+1)(3x-4) = 0
So the solutions are x = -1/2 and x = 4/3
