How to factor 4x^2-12=2x

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

Step-by-step explanation:

Given

4x² - 12 = 2x (subtract 2x from both sides)

4x² - 2x - 12 = 0 ← factor out 2 from each term

2 (2x² - x - 6) = 0

To 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 = 2 * - 6 = - 12 and sum = - 1

The factors are - 4 and + 3

Use these factors to split the x - term

2x² - 4x + 3x - 6 (factor the first/second and third/fourth terms)

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

(x - 2) (2x + 3), thus

2x² - x - 6 = (x - 2) (2x + 3) and

4x² - 2x - 12 = 0

2 (x - 2) (2x + 3) = 0 ← in factored form