What are the solutions to 6x^2-5x-4=0

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