1. |x^2-3x+3|=3

Question

2. |x^2+2x+1|=-4
3. |3x+2|+3=0

Answer 1

#2 and #3 are trick questions, since |x| >= 0 for all x

|x^2-3x+3|=3
x^2-3x+3=3 or -(x^2-3x+3)=3

In the first case,

x^2-3x+3=3
x^2-2x = 0
x(x-2) = 0
x = 0 or 2

In the second case,

-(x^2-3x+3)=3
x^2-3x+3 = -3
x^2 - 3x + 6 = 0
no real x satisfies the equation

final answer: x = 0 or 2