Solve for r 6(-r+8)=-5(-13r+16)-14

$6 (- r + 8) = - 5 (- 13 r + 16) - 14$

Step 1

Simplify $6 (- r + 8)$ .

Rewrite.

$0 + 0 + 6 (- r + 8) = - 5 (- 13 r + 16) - 14$

Simplify by adding zeros.

$6 (- r + 8) = - 5 (- 13 r + 16) - 14$

Apply the distributive property.

$6 (- r) + 6 \cdot 8 = - 5 (- 13 r + 16) - 14$

Multiply.

Multiply $- 1$ by $6$ .

$- 6 r + 6 \cdot 8 = - 5 (- 13 r + 16) - 14$

Multiply $6$ by $8$ .

$- 6 r + 48 = - 5 (- 13 r + 16) - 14$

Step 2

Simplify $- 5 (- 13 r + 16) - 14$ .

Simplify each term.

Apply the distributive property.

$- 6 r + 48 = - 5 (- 13 r) - 5 \cdot 16 - 14$

Multiply $- 13$ by $- 5$ .

$- 6 r + 48 = 65 r - 5 \cdot 16 - 14$

Multiply $- 5$ by $16$ .

$- 6 r + 48 = 65 r - 80 - 14$

Subtract $14$ from $- 80$ .

$- 6 r + 48 = 65 r - 94$

Step 3

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

Subtract $65 r$ from both sides of the equation.

$- 6 r + 48 - 65 r = - 94$

Subtract $65 r$ from $- 6 r$ .

$- 71 r + 48 = - 94$

Step 4

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

Subtract $48$ from both sides of the equation.

$- 71 r = - 94 - 48$

Subtract $48$ from $- 94$ .

$- 71 r = - 142$

Step 5

Divide each term in $- 71 r = - 142$ by $- 71$ and simplify.

Divide each term in $- 71 r = - 142$ by $- 71$ .

$\frac{- 71 r}{- 71} = \frac{- 142}{- 71}$

Simplify the left side.

Cancel the common factor of $- 71$ .

Cancel the common factor.

$\frac{- 71 r}{- 71} = \frac{- 142}{- 71}$

Divide $r$ by $1$ .

$r = \frac{- 142}{- 71}$

Simplify the right side.

Divide $- 142$ by $- 71$ .

$r = 2$

Solve for r 6(-r+8)=-5(-13r+16)-14

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