6x^2-11x-10=(3x+2)(2x+k)

What is the question?

what is the value of k in the equation

6x^2-11x-10=(3x+2)(2x+k)

6x^2-11x-10=6x^2 + 4x + 3kx + 2k

looks like 2k = -10
k = -5

Does that work for the middle term?
is -11x = 4x+3(-5)x
is -11x = 4x - 15x ? YEAH

k=-5

To find the value of k in the equation 6x^2-11x-10=(3x+2)(2x+k), you need to equate the two expressions on both sides of the equation.

First, expand the right side of the equation by multiplying (3x+2) and (2x+k):
(3x+2)(2x+k) = 6x^2 + 3xk + 4x + 2k

Now, equate this expanded expression to the left side of the equation:
6x^2 + 3xk + 4x + 2k = 6x^2 - 11x - 10

Since the equations are equal, the corresponding coefficients of the variables on both sides should also be equal.

Let's compare the coefficients for x^2:
For the left side: 6
For the right side: 6

The coefficients for x^2 are equal, so let's move on.

Next, compare the coefficients for x:
For the left side: 0 (no x term)
For the right side: -11

The coefficients for x are not equal, so we can ignore them for now.

Finally, compare the constant terms:
For the left side: -10
For the right side: 2k

Now, set the constant terms equal to each other and solve for k:
-10 = 2k

Divide both sides by 2:
-5 = k

Therefore, the value of k in the equation 6x^2-11x-10=(3x+2)(2x+k) is k = -5.