Solve for r 4(3r-2)=-3(r+7)

$4 (3 r - 2) = - 3 (r + 7)$

Step 1

Simplify $4 (3 r - 2)$ .

Start simplifying.

$0 + 0 + 4 (3 r - 2) = - 3 (r + 7)$

Simplify by adding zeros.

$4 (3 r - 2) = - 3 (r + 7)$

Apply the distributive property.

$4 (3 r) + 4 \cdot - 2 = - 3 (r + 7)$

Multiply.

Multiply $3$ by $4$ .

$12 r + 4 \cdot - 2 = - 3 (r + 7)$

Multiply $4$ by $- 2$ .

$12 r - 8 = - 3 (r + 7)$

Step 2

Simplify $- 3 (r + 7)$ .

Apply the distributive property.

$12 r - 8 = - 3 r - 3 \cdot 7$

Multiply $- 3$ by $7$ .

$12 r - 8 = - 3 r - 21$

Step 3

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

Add $3 r$ to both sides of the equation.

$12 r - 8 + 3 r = - 21$

Add $12 r$ and $3 r$ .

$15 r - 8 = - 21$

Step 4

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

Add $8$ to both sides of the equation.

$15 r = - 21 + 8$

Add $- 21$ and $8$ .

$15 r = - 13$

Step 5

Divide each term in $15 r = - 13$ by $15$ and simplify.

Divide each term in $15 r = - 13$ by $15$ .

$\frac{15 r}{15} = \frac{- 13}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 r}{15} = \frac{- 13}{15}$

Divide $r$ by $1$ .

$r = \frac{- 13}{15}$

Simplify the right side.

Move the negative in front of the fraction.

$r = - \frac{13}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{13}{15}$

Decimal Form:

$r = - 0.8\overline{6}$

Solve for r 4(3r-2)=-3(r+7)

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