Solve for t 5(2t-1)+3=3(3t+2)

$5 (2 t - 1) + 3 = 3 (3 t + 2)$

Step 1

Simplify $5 (2 t - 1) + 3$ .

Simplify each term.

Apply the distributive property.

$5 (2 t) + 5 \cdot - 1 + 3 = 3 (3 t + 2)$

Multiply $2$ by $5$ .

$10 t + 5 \cdot - 1 + 3 = 3 (3 t + 2)$

Multiply $5$ by $- 1$ .

$10 t - 5 + 3 = 3 (3 t + 2)$

Add $- 5$ and $3$ .

$10 t - 2 = 3 (3 t + 2)$

Step 2

Simplify $3 (3 t + 2)$ .

Apply the distributive property.

$10 t - 2 = 3 (3 t) + 3 \cdot 2$

Multiply.

Multiply $3$ by $3$ .

$10 t - 2 = 9 t + 3 \cdot 2$

Multiply $3$ by $2$ .

$10 t - 2 = 9 t + 6$

Step 3

Move all terms containing $t$ to the left side of the equation.

Subtract $9 t$ from both sides of the equation.

$10 t - 2 - 9 t = 6$

Subtract $9 t$ from $10 t$ .

$t - 2 = 6$

Step 4

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

Add $2$ to both sides of the equation.

$t = 6 + 2$

Add $6$ and $2$ .

$t = 8$