Solve by Factoring 3(x-2)-5x=-2(x+3)

$3 (x - 2) - 5 x = - 2 (x + 3)$

Step 1

Add $2 (x + 3)$ to both sides of the equation.

$3 (x - 2) - 5 x + 2 (x + 3) = 0$

Step 2

Simplify $3 (x - 2) - 5 x + 2 (x + 3)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 - 5 x + 2 (x + 3) = 0$

Multiply $3$ by $- 2$ .

$3 x - 6 - 5 x + 2 (x + 3) = 0$

Apply the distributive property.

$3 x - 6 - 5 x + 2 x + 2 \cdot 3 = 0$

Multiply $2$ by $3$ .

$3 x - 6 - 5 x + 2 x + 6 = 0$

Combine the opposite terms in $3 x - 6 - 5 x + 2 x + 6$ .

Add $- 6$ and $6$ .

$3 x - 5 x + 2 x + 0 = 0$

Add $3 x - 5 x + 2 x$ and $0$ .

$3 x - 5 x + 2 x = 0$

Subtract $5 x$ from $3 x$ .

$- 2 x + 2 x = 0$

Add $- 2 x$ and $2 x$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true