Solve v=-2(3a-b)+3(b-2c)

$$v = - 2 ( 3 a - b ) + 3 ( b - 2 c )$$

Solve for a

$$a=\frac{5b}{6}-\frac{v}{6}-c$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by 3a-b.

$$v=-6a+2b+3\left(b-2c\right)$$

Use the distributive property to multiply 3 by b-2c.

$$v=-6a+2b+3b-6c$$

Combine 2b and 3b to get 5b.

$$v=-6a+5b-6c$$

Swap sides so that all variable terms are on the left hand side.

$$-6a+5b-6c=v$$

Subtract 5b from both sides.

$$-6a-6c=v-5b$$

Add 6c to both sides.

$$-6a=v-5b+6c$$

The equation is in standard form.

$$-6a=v+6c-5b$$

Divide both sides by -6.

$$\frac{-6a}{-6}=\frac{v+6c-5b}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$a=\frac{v+6c-5b}{-6}$$

Divide v-5b+6c by -6.

$$a=\frac{5b}{6}-\frac{v}{6}-c$$

Solve for b

$$b=\frac{v+6a+6c}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by 3a-b.

$$v=-6a+2b+3\left(b-2c\right)$$

Use the distributive property to multiply 3 by b-2c.

$$v=-6a+2b+3b-6c$$

Combine 2b and 3b to get 5b.

$$v=-6a+5b-6c$$

Swap sides so that all variable terms are on the left hand side.

$$-6a+5b-6c=v$$

Add 6a to both sides.

$$5b-6c=v+6a$$

Add 6c to both sides.

$$5b=v+6a+6c$$

Divide both sides by 5.

$$\frac{5b}{5}=\frac{v+6a+6c}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$b=\frac{v+6a+6c}{5}$$