Find All Complex Solutions 3(x-2)=22-x

$3 (x - 2) = 22 - x$

Step 1

Move all the expressions to the left side of the equation.

Subtract $22$ from both sides of the equation.

$3 (x - 2) - 22 = - x$

Add $x$ to both sides of the equation.

$3 (x - 2) - 22 + x = 0$

Step 2

Simplify $3 (x - 2) - 22 + x$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 - 22 + x = 0$

Multiply $3$ by $- 2$ .

$3 x - 6 - 22 + x = 0$

Add $3 x$ and $x$ .

$4 x - 6 - 22 = 0$

Subtract $22$ from $- 6$ .

$4 x - 28 = 0$

Step 3

Factor $4$ out of $4 x - 28$ .

Factor $4$ out of $4 x$ .

$4 (x) - 28 = 0$

Factor $4$ out of $- 28$ .

$4 x + 4 \cdot - 7 = 0$

Factor $4$ out of $4 x + 4 \cdot - 7$ .

$4 (x - 7) = 0$

Step 4

Divide each term in $4 (x - 7) = 0$ by $4$ and simplify.

Divide each term in $4 (x - 7) = 0$ by $4$ .

$\frac{4 (x - 7)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (x - 7)}{4} = \frac{0}{4}$

Divide $x - 7$ by $1$ .

$x - 7 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x - 7 = 0$

Step 5

Add $7$ to both sides of the equation.

$x = 7$