Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.

Step-by-step explanation:

So we have the trinomial:

First, factor out a 2:

Now, factor within the parentheses.

To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b

(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.

-5 and 2 works. Therefore:

Replace -3x with 2x and -5x:

Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:

Grouping:

And we're done!

The red arrows on the black lines indicate that these two lines are parallel. The angles that are given in blue are called same-side supplementary angles. That means that when the value of these two angles are added, the sum would equal 180. In order to find x, an equation will be needed to be solved where the sum of the values of the angles equals 180:

(72) + (7x + 24) = 180
72 + 7x + 24 = 180

Like every equation, make sure to combine all like terms.
7x + 96=180
7x = 84

In order to achieve the value of x alone, divide both sides by 7.

x = 84/7

Final x = 12