Solve for z -6(17z+16)=9(-11z-10)+3z

$- 6 (17 z + 16) = 9 (- 11 z - 10) + 3 z$

Step 1

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

$9 (- 11 z - 10) + 3 z = - 6 (17 z + 16)$

Step 2

Simplify $9 (- 11 z - 10) + 3 z$ .

Simplify each term.

Apply the distributive property.

$9 (- 11 z) + 9 \cdot - 10 + 3 z = - 6 (17 z + 16)$

Multiply $- 11$ by $9$ .

$- 99 z + 9 \cdot - 10 + 3 z = - 6 (17 z + 16)$

Multiply $9$ by $- 10$ .

$- 99 z - 90 + 3 z = - 6 (17 z + 16)$

Add $- 99 z$ and $3 z$ .

$- 96 z - 90 = - 6 (17 z + 16)$

Step 3

Simplify $- 6 (17 z + 16)$ .

Apply the distributive property.

$- 96 z - 90 = - 6 (17 z) - 6 \cdot 16$

Multiply.

Multiply $17$ by $- 6$ .

$- 96 z - 90 = - 102 z - 6 \cdot 16$

Multiply $- 6$ by $16$ .

$- 96 z - 90 = - 102 z - 96$

Step 4

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

Add $102 z$ to both sides of the equation.

$- 96 z - 90 + 102 z = - 96$

Add $- 96 z$ and $102 z$ .

$6 z - 90 = - 96$

Step 5

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

Add $90$ to both sides of the equation.

$6 z = - 96 + 90$

Add $- 96$ and $90$ .

$6 z = - 6$

Step 6

Divide each term in $6 z = - 6$ by $6$ and simplify.

Divide each term in $6 z = - 6$ by $6$ .

$\frac{6 z}{6} = \frac{- 6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 z}{6} = \frac{- 6}{6}$

Divide $z$ by $1$ .

$z = \frac{- 6}{6}$

Simplify the right side.

Divide $- 6$ by $6$ .

$z = - 1$

Solve for z -6(17z+16)=9(-11z-10)+3z

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