Is my working correct?

Question: Find the eigenvalues and the corresponding eigenspaces for matrix A:

A=

6 -4

3 -1

|A - lambda * I| = 0

6-lambda -4

3 -1-lambda

(6-lambda)(-1-lambda) - (3)(-4)

-6 -6*lambda + lambda + lambda^2 + 12

6 -5*lambda + lambda^2

Factorize 6 -5*lambda + lambda^2

(lambda - 3)(lambda - 2)

Eigenvalues of A:

lambda = 3

lambda = 2

E(3) =

6x - 4y = 3x

3x - y = 3y

-4y = -3x

3x = 4y

Span = ?

The eigenspaces are ?

E(2) =

6x - 4y = 2x

3x - y = 2y

-4y = -4x

3x = 3y

Span = ?

The eigenspaces are ?

Where did I go wrong? How do I find the eigenvalues, what is the "span", and how do I find it?