Solve for x -21=3(-3x+6)+7(1-2x)

$- 21 = 3 (- 3 x + 6) + 7 (1 - 2 x)$

Step 1

Rewrite the equation as $3 (- 3 x + 6) + 7 (1 - 2 x) = - 21$ .

$3 (- 3 x + 6) + 7 (1 - 2 x) = - 21$

Step 2

Simplify $3 (- 3 x + 6) + 7 (1 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$3 (- 3 x) + 3 \cdot 6 + 7 (1 - 2 x) = - 21$

Multiply $- 3$ by $3$ .

$- 9 x + 3 \cdot 6 + 7 (1 - 2 x) = - 21$

Multiply $3$ by $6$ .

$- 9 x + 18 + 7 (1 - 2 x) = - 21$

Apply the distributive property.

$- 9 x + 18 + 7 \cdot 1 + 7 (- 2 x) = - 21$

Multiply $7$ by $1$ .

$- 9 x + 18 + 7 + 7 (- 2 x) = - 21$

Multiply $- 2$ by $7$ .

$- 9 x + 18 + 7 - 14 x = - 21$

Simplify by adding terms.

Subtract $14 x$ from $- 9 x$ .

$- 23 x + 18 + 7 = - 21$

Add $18$ and $7$ .

$- 23 x + 25 = - 21$

Step 3

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

Subtract $25$ from both sides of the equation.

$- 23 x = - 21 - 25$

Subtract $25$ from $- 21$ .

$- 23 x = - 46$

Step 4

Divide each term in $- 23 x = - 46$ by $- 23$ and simplify.

Divide each term in $- 23 x = - 46$ by $- 23$ .

$\frac{- 23 x}{- 23} = \frac{- 46}{- 23}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 x}{- 23} = \frac{- 46}{- 23}$

Divide $x$ by $1$ .

$x = \frac{- 46}{- 23}$

Simplify the right side.

Divide $- 46$ by $- 23$ .

$x = 2$