Factorise the equation 6x²-5x-6.

A quadratic expression is a polynomial of degree 2. We use the middle term factorization to solve this problem.

Answer: The factors of 6x² - 5x- 6 are (2x-3) (3x+2)

Let us proceed by using middle term factorization.

Explanation:

Step 1: Multiply the first term by the constant term, i.e., (6x² and -6) = -36x²

Step 2: Find the two factors of -36x² such that their sum is equal to the middle term, i.e., -5x.

Hence, two such factors are -9x and 4x

The product of -9x and 4x = -36x²

The sum of -9x and 4x = -5x

Thus, by splitting the middle term we have,

6x² - 9x + 4x - 6=0.     

⇒ 3x(2x-3) + 2(2x-3) = 0

⇒ (2x-3)(3x+2) = 0

Thus, the factors of 6x² - 5x - 6 are (2x-3) (3x+2).