Find eigenvalues and eigenvectors of this matrix

I found the eigenvalue λ_{1}=-3 and λ_{2}=6

When I added λ_{1}=-3 to the matrix, I have the equation system like this

x_{1}-2x_{2}+2x_{3}=0

-2x_{1}+4x_{2}-4x_{3}=0

2x_{1}-4x_{2}+4x_{3}=0

I don't know how to solve this equation system to figure out x_{1},x_{2},x_{3 }and eigenvector. Please help me!