Solve for t 5(2t-3)-7.5t=0.5(12-t)

$5 (2 t - 3) - 7.5 t = 0.5 (12 - t)$

Simplify $5 (2 t - 3) - 7.5 t$ .

Simplify each term.

Apply the distributive property.

$5 (2 t) + 5 \cdot - 3 - 7.5 t = 0.5 (12 - t)$

Multiply $2$ by $5$ .

$10 t + 5 \cdot - 3 - 7.5 t = 0.5 (12 - t)$

Multiply $5$ by $- 3$ .

$10 t - 15 - 7.5 t = 0.5 (12 - t)$

Subtract $7.5 t$ from $10 t$ .

$2.5 t - 15 = 0.5 (12 - t)$

Simplify $0.5 (12 - t)$ .

Apply the distributive property.

$2.5 t - 15 = 0.5 \cdot 12 + 0.5 (- t)$

Multiply.

Multiply $0.5$ by $12$ .

$2.5 t - 15 = 6 + 0.5 (- t)$

Multiply $- 1$ by $0.5$ .

$2.5 t - 15 = 6 - 0.5 t$

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

Add $0.5 t$ to both sides of the equation.

$2.5 t - 15 + 0.5 t = 6$

Add $2.5 t$ and $0.5 t$ .

$3 t - 15 = 6$

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

Add $15$ to both sides of the equation.

$3 t = 6 + 15$

Add $6$ and $15$ .

$3 t = 21$

Divide each term in $3 t = 21$ by $3$ and simplify.

Divide each term in $3 t = 21$ by $3$ .

$\frac{3 t}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{21}{3}$

Divide $t$ by $1$ .

$t = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$t = 7$