I need help with a quadratic equation..?

12x^2 = 5x + 2
12x^2 - 5x - 2 = 0
12x^2 - 8x + 3x - 2 = 0 ****
4x(3x - 2) + 1(3x - 2) = 0
(3x - 2)(4x + 1) = 0

so either 3x - 2 = 0 ==> x = 2/3
or 4x + 1 = 0 ==> x = -1/4


**** in the ac method, you're looking for factors of ac = 12(-2) = -24 that add to b = -5

here, -8 x 3 = -24 and -8 + 3 = -5
so split -5x = -8x + 3x , then factor by grouping

two solutions: x = 2/3 or x = -1/4

12x² = 5x + 2
12x² -5x - 2 = 0
(4x + 1)(3x - 2)

4x + 1 = 0
x = -1/4

3x - 2 = 0
x = 2/3

12x^2-5x-2 = 0
(4x+1)(3x-2) = 0
x = 2/3 or -1/4