Another one. Solve for x. x/(2x+1) - 1 = -4/7(x-2)

I know the answers are -6/7 and 3, but how do I determine this? Please show all work so I can fully understand the answer. Thank you!

From the given answers it is clear that the (x - 2) on the right is part of the denominator so it should be written as

x/(2x + 1) - 1 = -4/[7(x - 2)] ----> x/(2x + 1) - 1 = -4/(7x - 14)

Multiply everything by (2x + 1) to get
x - 1*(2x + 1) = -4(2x + 1)/(7x - 14)----> -(x + 1) = -4(2x + 1)/(7x - 14)

Change signs both sides to get
x + 1 = 4(2x + 1)/(7x - 14)

Multiply everything by 7x - 14 to get
(x + 1)(7x - 14) = 4(2x + 1)

7x^2 - 7x - 14 = 8x + 4 ----> 7x^2 - 15x - 18 = 0

----> (7x + 6)(x - 3) = 0 ----> 7x = 6 = 0 or x - 3 = 0 ----> x = -6/7 or 3

will assume you meant

x/(2x+1) -1 = -4/(7(x-2))
x/(2x+1) - 1 = -4/(7x-14) multiply by (2x+1)(7x-14)

x(7x-14) - (2x+1)(7x-14) = -4(2x+1)
7x^2 - 14x -14x^2 +21x + 14 = -8x -4
-7x^2 + 7x +14 = -8x - 4
-7x^2 +15x + 18 = 0
use the quadradic eqaution [-15 +/- sqrt(15^2-4(-7)(18)] / 2(-7)

[15 +/- 27] /-14 or -6/7 and 3