What is 12x2 + 5x-2=0?

Pls help me with this question

I always get these type of questions wrong and I do not know why here is my working out

12x2 + 5x-2=0

(12x2-3)+(8x-2)
3x(4x-1)+2(4x-1)
x= 1/4
but the answers say its x=1/4 or x= -2/3
Pls what am i doing wrong?

12x^2 + 5x - 2 = 0 <-------------> ax^2 + bx + c = 0

Factor: (3x + __ ) ( 4x + __) = 0

The values must add or subtract to "5". We have "-2" so we have -2 and 1 or 1 and -2 to choose from...unless of course, I should have factored out a 6 and a 2 from the 12.

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

Foil (first, outer, inner, last [multiplication stuff) it to make sure that I solved it correctly:

3x(4x) + 3x(-1) + 2(4x) + 2(-1) = 12x^2 - 3x + 8x - 2 = 12x^2 + 5x - 2 = 0 ....yay! It's right!

3x + 2 = 0

3x + 2 - 2 = - 2

3x = -2

3x / 3 = -2 / 3

x = -2/3

4x - 1 = 0

4x - 1 + 1 = 0 + 1

4x = 1

4x / 4 = 1 / 4

Solutions: x = 1/4 and x = -2/3

You didn't factor it correctly. But, yes, 1/4 is indeed a solution.

You did factor it. But, you did not factor it completely.

Also, you could use the quadratic equation on this:

Note that...

ax^2 + bx + c = 0 <---------------> 12x^2 + 5x - 2 = 0 <------------> an equation for a parabola.

Note: a = 12, b = 5, and c = -2

Anytime, you have a variable raised to a squared power and that variable not raised to a power (well, technically to the oneth power, and a constant set equal to zero, you will either have two solutions or sometimes you solutions will be imaginary, and if that's the case, then you can't factor the equation, anyway. But, you could use the quadratic equation and it fails if you have any negative value under the square root in the quadratic equation.

The quadratic equation explained:

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