Solve by Factoring 2(x+2)+x=3(x-1)+6

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

Step 1

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

Subtract $3 (x - 1)$ from both sides of the equation.

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

Subtract $6$ from both sides of the equation.

$2 (x + 2) + x - 3 (x - 1) - 6 = 0$

Step 2

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

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 2 + x - 3 (x - 1) - 6 = 0$

Multiply $2$ by $2$ .

$2 x + 4 + x - 3 (x - 1) - 6 = 0$

Apply the distributive property.

$2 x + 4 + x - 3 x - 3 \cdot - 1 - 6 = 0$

Multiply $- 3$ by $- 1$ .

$2 x + 4 + x - 3 x + 3 - 6 = 0$

Add $2 x$ and $x$ .

$3 x + 4 - 3 x + 3 - 6 = 0$

Combine the opposite terms in $3 x + 4 - 3 x + 3 - 6$ .

Subtract $3 x$ from $3 x$ .

$0 + 4 + 3 - 6 = 0$

Add $0$ and $4$ .

$4 + 3 - 6 = 0$

Add $4$ and $3$ .

$7 - 6 = 0$

Subtract $6$ from $7$ .

$1 = 0$

Step 3

Since $1 \neq 0$ , there are no solutions.

No solution