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