Factoring Math Equations help

7 (x^2 + 2x - 3) someone told me its not fully factored and had to be 7 (x+3) (x-1) but when do i have to do this? everytime? for example 10 (4m^2+3x-1) do i still have to factor that?

Yes you do, you need to factor those questions until fully factored.

10(4m^2+3x-1) <-- Can't be factored no more. why? i think you wrote the question wrong, 4m is 4x? if so yes it needs to be factored more. If that's the case then,

10(4x^2+3x-1)
10[4x^2 + 4x - x - 1]
10[4x(x + 1) - (x + 1)]
10(4x - 1)(x + 1)

Factoring is simply doing FOIL backwards. You have to break the middle term into two terms. What multiplies to get -3 (third coefficient times first coefficient) and adds to get 2 (second coefficient)? 3 and -1! Break 2x into 3x-x:

7(x^2+3x-x-3)
7(x(x+3)-1(x+3))
7(x-1)(x+3)<====ANSWER

What multiplies to get -4 (third coefficient times first coefficitne) and adds to get 3 (second coefficient)? 4 and -1, so break 3x into 4x-x:

10(4x^2+4x-x-1)
10(4x(x+1)-1(x+1))
10(4x-1)(x+1)<====ANSWER

7(x^2 + 2x -3) =0 is the whole equation
now either 7=0 or x^ + 2x -3=0
but 7 is not equal to zero
so x^2+2x-3=0
x^2+3x-x-3=0
x(x+3)-1(x+3)=0
(x-1)(x+3)=0 so if the question says simplify the equation it is necessary but if it is not mentioned but still is better to do it.

You can sometimes factorise a quadratic (something with an x² in).
For example x² + 7x + 12 can be factorised into two brackets.
(x + 4)(x + 3).
For 4m² + 3m - 1 you can factorise it into:
(4m - 1 )(x + 1)