Solve for t -17-6(7t+18)=-20t+19+2t

$- 17 - 6 (7 t + 18) = - 20 t + 19 + 2 t$

Step 1

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

$- 20 t + 19 + 2 t = - 17 - 6 (7 t + 18)$

Step 2

Add $- 20 t$ and $2 t$ .

$- 18 t + 19 = - 17 - 6 (7 t + 18)$

Step 3

Simplify $- 17 - 6 (7 t + 18)$ .

Simplify each term.

Apply the distributive property.

$- 18 t + 19 = - 17 - 6 (7 t) - 6 \cdot 18$

Multiply $7$ by $- 6$ .

$- 18 t + 19 = - 17 - 42 t - 6 \cdot 18$

Multiply $- 6$ by $18$ .

$- 18 t + 19 = - 17 - 42 t - 108$

Subtract $108$ from $- 17$ .

$- 18 t + 19 = - 42 t - 125$

Step 4

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

Add $42 t$ to both sides of the equation.

$- 18 t + 19 + 42 t = - 125$

Add $- 18 t$ and $42 t$ .

$24 t + 19 = - 125$

Step 5

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

Subtract $19$ from both sides of the equation.

$24 t = - 125 - 19$

Subtract $19$ from $- 125$ .

$24 t = - 144$

Step 6

Divide each term in $24 t = - 144$ by $24$ and simplify.

Divide each term in $24 t = - 144$ by $24$ .

$\frac{24 t}{24} = \frac{- 144}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 t}{24} = \frac{- 144}{24}$

Divide $t$ by $1$ .

$t = \frac{- 144}{24}$

Simplify the right side.

Divide $- 144$ by $24$ .

$t = - 6$