Factorize the quadratic expression: 6x2−21x+186x2-21x+18.

Sure, let's factorize the quadratic expression step by step:

1. First, write down the quadratic expression: 6x^2 - 21x + 18

2. The quadratic expression is in the form ax^2 + bx + c. In this case, a = 6, b = -21, and c = 18.

3. We need to find two numbers that multiply to give ac (which is 6*18 = 108) and add up to give b (which is -21).

4. The two numbers that satisfy these conditions are -9 and -12 (because -9*-12 = 108 and -9 + -12 = -21).

5. Rewrite the middle term of the quadratic expression as the sum of the terms -9x and -12x: 6x^2 - 9x - 12x + 18

6. Factor by grouping: 3x(2x - 3) - 6(2x - 3)

7. Notice that the terms in the parentheses are the same, so we can factor them out: (2x - 3)(3x - 6)

So, the factorized form of the quadratic expression 6x^2 - 21x + 18 is (2x - 3)(3x - 6).