(х+2)²+2(х+2)-3=0

Let's solve the equation step by step.

First, let's simplify the equation. (х+2)² + 2(х+2) - 3 = 0 Simplify the terms: (х+2)(х+2) + 2(х+2) - 3 = 0 (х+2)² + 2(х+2) - 3 = 0 (х+2)(х+2) + 2х + 4 - 3 = 0 (х+2)(х+2) + 2х + 1 = 0

Next, let's apply the distributive property to simplify further: (х² + 4х + 4) + 2х + 1 = 0 х² + 4х + 4 + 2х + 1 = 0 х² + 6х + 5 = 0

Now, let's solve the quadratic equation. We can either factorize it or use the quadratic formula.

Factoring: (х + 1)(х + 5) = 0

So, either х + 1 = 0 or х + 5 = 0 If х + 1 = 0, then х = -1 If х + 5 = 0, then х = -5

Therefore, the solutions to the equation are х = -1 and х = -5.