What are the factors of the equation 24x^2=9-30x?

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

Step-by-step explanation:

Rearrange the equation into standard form

Subtract 9 - 30x from both sides

24x² + 30x - 9 = 0 ← in standard form

Take out 3 as a common factor

3 (8x² + 10x - 3) = 0 ← factor the quadratic

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 = 8 * - 3 = - 24, sum = 10

The factors are - 2 and + 12

Use these factors to replace the x - term, that is

8x² - 2x + 12x - 3 (factor the first/second and third/fourth terms)

2x (4x - 1) + 3 (4x - 1) ← take out the common factor (4x - 1)

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

24x² + 30x - 9 = 3 (4x - 1) (2x + 3) ← in factored form