Factor completely and show all steps? How do you factor 5x^2 -7x -6?

5x^2-7x-6
=5x^2-10x+3x-6
=5x(x-2)+3(x-2)
=(x-2)(5x+3)

5x^2 - 7x - 6

= 5x^2 - 10x + 3x - 6

= 5x(x - 2) + 3(x - 2)

= (5x + 3)(x - 2)

I hope this helps.

Edit: Adding a more complete explanation of factoring quadratics to reflect the useful comment by one of my good colleagues and great contributors to this forum.

Factoring quadratics:
A quadratic equation in general is defined as:
Ax^2 + Bx + C = 0
Example (easy case when A = 1)
x^2 + 5x + 6 => look for two numbers that add to +5, multiply to + 6 i.e. (3 & 2)
=(x + 3)(x + 2)

The AC Method:
What can we do when the leading coefficient is not 1?
We use an extension of factoring by grouping called the AC method.
Step by Step method for factoring Ax^2 + Bx + C :
Step 1. Multiply together AC and list the factors of AC.
Step 2. Find a pair that adds to B. If you can't find such pair the quadratic is a prime and does not factor.
Step 3. Rewrite the middle term as a sum of terms whose coefficients are the chosen pair.
Step 4. Factor by grouping.
Remember you should always first pull out the GCF.

Examples:
1) 2x^2 + 5x - 25
AC = (2)(-25) = -50
the pairs are:
(1,-50), (-1,50), (2,-25), (-2,25), (5,-10) and (-5,10).
We see that: -5 + 10 = 5 hence we choose the pair (-5,10)
We write:
2x^2 - 5x + 10x - 25
= (2x^2 - 5x) + (10x - 25)
= x(2x - 5) + 5 (2x - 5)
= (x + 5) (2x - 5)

2) 9x^2- 49x - 30
AC = (9)(-30) = -270 => Hint : find the pairs that add to -49 i.e, (-54 , 5):
= 9x^2 - 54x + 5x - 30
= 9x(x - 6) + 5(x - 6)
= (x - 6)(9x + 5)

Regards.

5x²–7x–6
(5x+3)(x–2)

(5x+3)(x-2)

This is fairly simple: (ax+b)(cx+d) = 5x^2-7x-6

ac = 5
ad + bc = -7
bd = -6

So we know a = 5 and c = 1 is only possibility (note that a and c are interchangeable - what matters is how a/d values and b/c relate once we set which value is which
This gives us 5d + b = -7 and bd = -6. b = 3 and d = -2.