Solve for t 2(2t-3)+t=12-t

$2 (2 t - 3) + t = 12 - t$

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

$4 t + 2 \cdot - 3 + t = 12 - t$

Multiply $2$ by $- 3$ .

$4 t - 6 + t = 12 - t$

Add $4 t$ and $t$ .

$5 t - 6 = 12 - t$

Step 2

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

Add $t$ to both sides of the equation.

$5 t - 6 + t = 12$

Add $5 t$ and $t$ .

$6 t - 6 = 12$

Step 3

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

Add $6$ to both sides of the equation.

$6 t = 12 + 6$

Add $12$ and $6$ .

$6 t = 18$

Step 4

Divide each term in $6 t = 18$ by $6$ and simplify.

Divide each term in $6 t = 18$ by $6$ .

$\frac{6 t}{6} = \frac{18}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 t}{6} = \frac{18}{6}$

Divide $t$ by $1$ .

$t = \frac{18}{6}$

Simplify the right side.

Divide $18$ by $6$ .

$t = 3$