Solve for x 3(3x-1)+2(3-x)=0

$3 (3 x - 1) + 2 (3 - x) = 0$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 (3 x) + 3 \cdot - 1 + 2 (3 - x) = 0$

Multiply $3$ by $3$ .

$9 x + 3 \cdot - 1 + 2 (3 - x) = 0$

Multiply $3$ by $- 1$ .

$9 x - 3 + 2 (3 - x) = 0$

Apply the distributive property.

$9 x - 3 + 2 \cdot 3 + 2 (- x) = 0$

Multiply $2$ by $3$ .

$9 x - 3 + 6 + 2 (- x) = 0$

Multiply $- 1$ by $2$ .

$9 x - 3 + 6 - 2 x = 0$

$9 x - 3 + 6 - 2 x = 0$

Simplify by adding terms.

Subtract $2 x$ from $9 x$ .

$7 x - 3 + 6 = 0$

Add $- 3$ and $6$ .

$7 x + 3 = 0$

$7 x + 3 = 0$

$7 x + 3 = 0$

Step 2

Subtract $3$ from both sides of the equation.

$7 x = - 3$

Step 3

Divide each term in $7 x = - 3$ by $7$ and simplify.

Divide each term in $7 x = - 3$ by $7$ .

$\frac{7 x}{7} = \frac{- 3}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 3}{7}$

Divide $x$ by $1$ .

$x = \frac{- 3}{7}$

$x = \frac{- 3}{7}$

$x = \frac{- 3}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{7}$

$x = - \frac{3}{7}$

$x = - \frac{3}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{7}$

Decimal Form:

$x = - 0.\overline{428571}$

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