Factor: 7x^3 +28x^2 -21x^2 -84x

can someone give me a step by step solution for this, please? thanks!

Factor in pairs:

7x³ + 28x² − 21x² − 84x

= 7x² (x + 4) − 21x (x + 4) ----> factor out (x + 4)

= (x + 4) (7x² − 21x) -----> factor out 7x from (7x² − 21x)

= 7x (x + 4) (x − 3)

First, simplify.
Then, look for a common factor throughout-

7x³ + 7x² - 84x

7x(x² + x - 12)

Then use rules for factoring trinomials.
F*F = x², L*L = 12 (ignore sign initially)
outer and inner product have difference of 1; larger of them is +, smaller is -

7x(x + 4)(x - 3)

7x^3 +28x^2 -21x^2 - 84x ... by inspection, all terms are divisible by 7x
= 7x(x^2 + 4x - 3x - 12)
= 7x(x^2 + x - 12) need two numbers that add to 1(coefficient of x) and multiply to -12, i.e. 4 and -3
= 7x(x + 4)(x - 3)

Factor out 7x^2 from 7x^3 and 28x^2 AND -21x from - 21x^2 - 84x:

7x^3 + 28x^2 - 21x^2 - 84x =
7x^2(x + 4) - 21x(x + 4) =

Now factor out (x + 4)
(x + 4)(7x^2 - 21x) =
7x(x + 4)(x - 3)