Factor the given expression completely and show your work. 6x^2-5x-21. Check your answer and show that work as well. PLSS SOLV GIVING BRAINIL

(2x + 3)(3x - 7)

Step-by-step explanation:

Factorize 6x² - 5x - 21

Find two numbers which are factors of the product of the coefficient of x² and the constant, and sum to the coefficient of x.  

coefficient of x² mulitplied by the constant = 6 x -21 = -126

So we need to find two numbers that multiply together to make -126 and sum to -5.

Factors of -126 that sum to -5:  9 and -14

As  9 x -14 = -126,  and   9 - 14 = -5

Rewrite the center term of the quadratic as these numbers, so - 5x becomes 9x - 14x:

⇒ 6x² + 9x - 14x - 21

Factorize each pair of terms, checking that the bracket created is the same:

⇒ 3x(2x + 3) - 7(2x + 3)

The first bracket is the common factor of (2x + 3) and the second bracket is the factorized terms outside of each bracket (3x - 7).  So the final factorization is:

(2x + 3)(3x - 7)

i believe that is true.

step-by-step explanation:

hope my answer has you if not i'm sorry.