How are these two discrete time signals equal?

How are these two signals equal?

What I have tried:

$$x[n] = (-3)(-2)(-2)^{n-1}u[n] + (-2)^{n-1}u[n]$$

$$-3(-2)^nu[n]=(-3)(-2)(-2)^{n-1}u[n]=6(-2)^{n-1}u[n]\tag{1}$$
The value of $$(1)$$ at $$n=0$$ is $$6/(-2)=-3$$, so we can rewrite it as
$$-3\delta[n]+6(-2)^{n-1}u[n-1]\tag{2}$$
Adding the second term $$(-2)^{n-1}u[n-1]$$ results in
$$x[n]=-3\delta[n]+7(-2)^{n-1}u[n-1]\tag{3}$$