Solve for t 7(t+3)-2=5(t-2)+5

$7 (t + 3) - 2 = 5 (t - 2) + 5$

Step 1

Simplify $7 (t + 3) - 2$ .

Simplify each term.

Apply the distributive property.

$7 t + 7 \cdot 3 - 2 = 5 (t - 2) + 5$

Multiply $7$ by $3$ .

$7 t + 21 - 2 = 5 (t - 2) + 5$

Subtract $2$ from $21$ .

$7 t + 19 = 5 (t - 2) + 5$

Step 2

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

Simplify each term.

Apply the distributive property.

$7 t + 19 = 5 t + 5 \cdot - 2 + 5$

Multiply $5$ by $- 2$ .

$7 t + 19 = 5 t - 10 + 5$

Add $- 10$ and $5$ .

$7 t + 19 = 5 t - 5$

Step 3

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

Subtract $5 t$ from both sides of the equation.

$7 t + 19 - 5 t = - 5$

Subtract $5 t$ from $7 t$ .

$2 t + 19 = - 5$

Step 4

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

Subtract $19$ from both sides of the equation.

$2 t = - 5 - 19$

Subtract $19$ from $- 5$ .

$2 t = - 24$

Step 5

Divide each term in $2 t = - 24$ by $2$ and simplify.

Divide each term in $2 t = - 24$ by $2$ .

$\frac{2 t}{2} = \frac{- 24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t}{2} = \frac{- 24}{2}$

Divide $t$ by $1$ .

$t = \frac{- 24}{2}$

Simplify the right side.

Divide $- 24$ by $2$ .

$t = - 12$