To solve the equation (2x+1)^2 = 75, we can start by taking the square root of both sides:

√((2x+1)^2) = √75

Simplifying the left side:

2x+1 = ±√75

Next, we can subtract 1 from both sides:

2x = ±√75 - 1

Now, we can divide both sides by 2:

x = (±√75 - 1) / 2

Simplifying further:

x = (√75 - 1) / 2 or x = (-√75 - 1) / 2

Therefore, the solutions to the equation (2x+1)^2 = 75 are:

x = (√75 - 1) / 2 and x = (-√75 - 1) / 2