Solve for a -3a+6b=a+4b

$- 3 a + 6 b = a + 4 b$

Step 1

Move all terms containing $a$ to the left side of the equation.

Subtract $a$ from both sides of the equation.

$- 3 a + 6 b - a = 4 b$

Subtract $a$ from $- 3 a$ .

$- 4 a + 6 b = 4 b$

Step 2

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

Subtract $6 b$ from both sides of the equation.

$- 4 a = 4 b - 6 b$

Subtract $6 b$ from $4 b$ .

$- 4 a = - 2 b$

Step 3

Divide each term in $- 4 a = - 2 b$ by $- 4$ and simplify.

Divide each term in $- 4 a = - 2 b$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{- 2 b}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{- 2 b}{- 4}$

Divide $a$ by $1$ .

$a = \frac{- 2 b}{- 4}$

Simplify the right side.

Cancel the common factor of $- 2$ and $- 4$ .

Factor $- 2$ out of $- 2 b$ .

$a = \frac{- 2 (b)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$a = \frac{- 2 (b)}{- 2 (2)}$

Cancel the common factor.

$a = \frac{- 2 b}{- 2 \cdot 2}$

Rewrite the expression.

$a = \frac{b}{2}$