Solve for n t(n)=-6+3(n-1)

$t (n) = - 6 + 3 (n - 1)$

Simplify $- 6 + 3 (n - 1)$ .

Simplify each term.

Apply the distributive property.

$t n = - 6 + 3 n + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$t n = - 6 + 3 n - 3$

Subtract $3$ from $- 6$ .

$t n = 3 n - 9$

Subtract $3 n$ from both sides of the equation.

$t n - 3 n = - 9$

Factor $n$ out of $t n - 3 n$ .

Factor $n$ out of $t n$ .

$n t - 3 n = - 9$

Factor $n$ out of $- 3 n$ .

$n t + n \cdot - 3 = - 9$

Factor $n$ out of $n t + n \cdot - 3$ .

$n (t - 3) = - 9$

Divide each term in $n (t - 3) = - 9$ by $t - 3$ and simplify.

Divide each term in $n (t - 3) = - 9$ by $t - 3$ .

$\frac{n (t - 3)}{t - 3} = \frac{- 9}{t - 3}$

Simplify the left side.

Cancel the common factor of $t - 3$ .

Cancel the common factor.

$\frac{n (t - 3)}{t - 3} = \frac{- 9}{t - 3}$

Divide $n$ by $1$ .

$n = \frac{- 9}{t - 3}$

Simplify the right side.

Move the negative in front of the fraction.

$n = - \frac{9}{t - 3}$