Find the value of k for which the quadratic equation kx(x - 2) + 6 = 0 has two real and equal roots.

The given equation can be written as $kx^2 - 2kx + 6 = 0$. For real and equal roots, the discriminant $D = b^2 - 4ac = 0$. Here $a = k$, $b = -2k$, and $c = 6$. So, $(-2k)^2 - 4(k)(6) = 0 \implies 4k^2 - 24k = 0 \implies 4k(k - 6) = 0$. Since $k \neq 0$ for a quadratic equation, we get $k = 6$.