Solve for t 2(2t+4)=34(24-8t)

$2 (2 t + 4) = 34 (24 - 8 t)$

Step 1

Simplify $2 (2 t + 4)$ .

Start simplifying.

$0 + 0 + 2 (2 t + 4) = 34 (24 - 8 t)$

Simplify by adding zeros.

$2 (2 t + 4) = 34 (24 - 8 t)$

Apply the distributive property.

$2 (2 t) + 2 \cdot 4 = 34 (24 - 8 t)$

Multiply.

Multiply $2$ by $2$ .

$4 t + 2 \cdot 4 = 34 (24 - 8 t)$

Multiply $2$ by $4$ .

$4 t + 8 = 34 (24 - 8 t)$

Step 2

Simplify $34 (24 - 8 t)$ .

Apply the distributive property.

$4 t + 8 = 34 \cdot 24 + 34 (- 8 t)$

Multiply.

Multiply $34$ by $24$ .

$4 t + 8 = 816 + 34 (- 8 t)$

Multiply $- 8$ by $34$ .

$4 t + 8 = 816 - 272 t$

Step 3

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

Add $272 t$ to both sides of the equation.

$4 t + 8 + 272 t = 816$

Add $4 t$ and $272 t$ .

$276 t + 8 = 816$

Step 4

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

Subtract $8$ from both sides of the equation.

$276 t = 816 - 8$

Subtract $8$ from $816$ .

$276 t = 808$

Step 5

Divide each term in $276 t = 808$ by $276$ and simplify.

Divide each term in $276 t = 808$ by $276$ .

$\frac{276 t}{276} = \frac{808}{276}$

Simplify the left side.

Cancel the common factor of $276$ .

Cancel the common factor.

$\frac{276 t}{276} = \frac{808}{276}$

Divide $t$ by $1$ .

$t = \frac{808}{276}$

Simplify the right side.

Cancel the common factor of $808$ and $276$ .

Factor $4$ out of $808$ .

$t = \frac{4 (202)}{276}$

Cancel the common factors.

Factor $4$ out of $276$ .

$t = \frac{4 \cdot 202}{4 \cdot 69}$

Cancel the common factor.

$t = \frac{4 \cdot 202}{4 \cdot 69}$

Rewrite the expression.

$t = \frac{202}{69}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{202}{69}$

Decimal Form:

$t = 2.92753623 \dots$

Mixed Number Form:

$t = 2 \frac{64}{69}$

Solve for t 2(2t+4)=34(24-8t)

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