Solve for t (3t+3)/5=6

$\frac{3 t + 3}{5} = 6$

Multiply both sides by $5$ .

$\frac{3 t + 3}{5} \cdot 5 = 6 \cdot 5$

Simplify.

Simplify the left side.

Simplify $\frac{3 t + 3}{5} \cdot 5$ .

Factor $3$ out of $3 t + 3$ .

Factor $3$ out of $3 t$ .

$\frac{3 (t) + 3}{5} \cdot 5 = 6 \cdot 5$

Factor $3$ out of $3$ .

$\frac{3 (t) + 3 (1)}{5} \cdot 5 = 6 \cdot 5$

Factor $3$ out of $3 (t) + 3 (1)$ .

$\frac{3 (t + 1)}{5} \cdot 5 = 6 \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 (t + 1)}{5} \cdot 5 = 6 \cdot 5$

Rewrite the expression.

$3 (t + 1) = 6 \cdot 5$

Apply the distributive property.

$3 t + 3 \cdot 1 = 6 \cdot 5$

Multiply $3$ by $1$ .

$3 t + 3 = 6 \cdot 5$

Simplify the right side.

Multiply $6$ by $5$ .

$3 t + 3 = 30$

Solve for $t$ .

Move all terms not containing $t$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$3 t = 30 - 3$

Subtract $3$ from $30$ .

$3 t = 27$

Divide each term in $3 t = 27$ by $3$ and simplify.

Divide each term in $3 t = 27$ by $3$ .

$\frac{3 t}{3} = \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{27}{3}$

Divide $t$ by $1$ .

$t = \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$t = 9$