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

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

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 3$ by $1$ .

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

Multiply $- 1$ by $- 3$ .

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

Add $2 t$ and $3 t$ .

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

Apply the distributive property.

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

Multiply $5$ by $- 2$ .

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

Multiply $- 2$ by $- 3$ .

$2 - 10 t + 6 = t$

Add $2$ and $6$ .

$- 10 t + 8 = t$

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

Subtract $t$ from both sides of the equation.

$- 10 t + 8 - t = 0$

Subtract $t$ from $- 10 t$ .

$- 11 t + 8 = 0$

Subtract $8$ from both sides of the equation.

$- 11 t = - 8$

Divide each term in $- 11 t = - 8$ by $- 11$ and simplify.

Divide each term in $- 11 t = - 8$ by $- 11$ .

$\frac{- 11 t}{- 11} = \frac{- 8}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 t}{- 11} = \frac{- 8}{- 11}$

Divide $t$ by $1$ .

$t = \frac{- 8}{- 11}$

Simplify the right side.

Dividing two negative values results in a positive value.

$t = \frac{8}{11}$

The result can be shown in multiple forms.

Exact Form:

$t = \frac{8}{11}$

Decimal Form:

$t = 0.\overline{72}$