(x+1)(2x-5)=0Not sure if I am heading in the right direction by x(2x-5)+1(2x-5)=0 2x^2-5x+1x-5=0

Hope you want to solve the equation (x+1)(2x-5) =
0.

We solve the equation to know the value of the variable for which
the equation is satisfied.

If a product a*b = 0, the a = 0 or b = 0.
this is the law of zer product.

Since (x+1)(2x - 5) = 0, then by the
law of zero product x+1 = 0 or 2x-5 = 0.

x+1 = 0 gives x=
-1.

2x-5 = 0 gives  2x= 5, or x= 5/2 =
2.5.

Therefore x = -1 or x = 2.5 are solution to (x+1)(2x-5) =
0.

What did  is writing the equation (x+1)(2x-5) = 0  in the
expanded form . But here is an error.

(x+1)(2x-5) =
x(2x-5)+1(2x-5).

(x+1)(2-5) =
2x^2-5x+2x-5.

(x+1)(2x-5) = 2x^2 - 3x-5.