Solve for r 4(3r+4)=-8(2r+5)

$4 (3 r + 4) = - 8 (2 r + 5)$

Step 1

Simplify $4 (3 r + 4)$ .

Rewrite.

$0 + 0 + 4 (3 r + 4) = - 8 (2 r + 5)$

Simplify by adding zeros.

$4 (3 r + 4) = - 8 (2 r + 5)$

Apply the distributive property.

$4 (3 r) + 4 \cdot 4 = - 8 (2 r + 5)$

Multiply.

Multiply $3$ by $4$ .

$12 r + 4 \cdot 4 = - 8 (2 r + 5)$

Multiply $4$ by $4$ .

$12 r + 16 = - 8 (2 r + 5)$

Step 2

Simplify $- 8 (2 r + 5)$ .

Apply the distributive property.

$12 r + 16 = - 8 (2 r) - 8 \cdot 5$

Multiply.

Multiply $2$ by $- 8$ .

$12 r + 16 = - 16 r - 8 \cdot 5$

Multiply $- 8$ by $5$ .

$12 r + 16 = - 16 r - 40$

Step 3

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

Add $16 r$ to both sides of the equation.

$12 r + 16 + 16 r = - 40$

Add $12 r$ and $16 r$ .

$28 r + 16 = - 40$

Step 4

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

Subtract $16$ from both sides of the equation.

$28 r = - 40 - 16$

Subtract $16$ from $- 40$ .

$28 r = - 56$

Step 5

Divide each term in $28 r = - 56$ by $28$ and simplify.

Divide each term in $28 r = - 56$ by $28$ .

$\frac{28 r}{28} = \frac{- 56}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 r}{28} = \frac{- 56}{28}$

Divide $r$ by $1$ .

$r = \frac{- 56}{28}$

Simplify the right side.

Divide $- 56$ by $28$ .

$r = - 2$

Solve for r 4(3r+4)=-8(2r+5)

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