Solve for r 3(7r-7)=-6+6r

$3 (7 r - 7) = - 6 + 6 r$

Step 1

Simplify $3 (7 r - 7)$ .

Rewrite.

$0 + 0 + 3 (7 r - 7) = - 6 + 6 r$

Simplify by adding zeros.

$3 (7 r - 7) = - 6 + 6 r$

Apply the distributive property.

$3 (7 r) + 3 \cdot - 7 = - 6 + 6 r$

Multiply.

Multiply $7$ by $3$ .

$21 r + 3 \cdot - 7 = - 6 + 6 r$

Multiply $3$ by $- 7$ .

$21 r - 21 = - 6 + 6 r$

Step 2

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

Subtract $6 r$ from both sides of the equation.

$21 r - 21 - 6 r = - 6$

Subtract $6 r$ from $21 r$ .

$15 r - 21 = - 6$

Step 3

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

Add $21$ to both sides of the equation.

$15 r = - 6 + 21$

Add $- 6$ and $21$ .

$15 r = 15$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Divide $15$ by $15$ .

$r = 1$