I don’t know how to solve this. Can anyone help me get the answer and the work

{ - , 12 }

Step-by-step explanation:

We can solve the equation by factoring it

3x² - 34x - 24 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 24 = - 72 and sum = - 34

The factors are - 36 and + 2

Use these factors to split the x- term

3x² - 36x + 2x - 24 = 0 ( factor the first/second and third/fourth terms )

3x(x - 12) + 2(x - 12) = 0 ← factor out (x - 12) from each term

(x - 12)(3x + 2) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = -

Thus the solution set is { - , 12 }