Solve 3z-2+6(1-z)=5(c-3z)-4a

$$3 z - 2 + 6 ( 1 - z ) = 5 ( c - 3 z ) - 4 a$$

Solve for a

$$a=\frac{5c}{4}-3z-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 1-z.

$$3z-2+6-6z=5\left(c-3z\right)-4a$$

Add -2 and 6 to get 4.

$$3z+4-6z=5\left(c-3z\right)-4a$$

Combine 3z and -6z to get -3z.

$$-3z+4=5\left(c-3z\right)-4a$$

Use the distributive property to multiply 5 by c-3z.

$$-3z+4=5c-15z-4a$$

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

$$5c-15z-4a=-3z+4$$

Subtract 5c from both sides.

$$-15z-4a=-3z+4-5c$$

Add 15z to both sides.

$$-4a=-3z+4-5c+15z$$

Combine -3z and 15z to get 12z.

$$-4a=12z+4-5c$$

The equation is in standard form.

$$-4a=12z-5c+4$$

Divide both sides by -4.

$$\frac{-4a}{-4}=\frac{12z-5c+4}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$a=\frac{12z-5c+4}{-4}$$

Divide 12z+4-5c by -4.

$$a=\frac{5c}{4}-3z-1$$

Solve for c

$$c=\frac{4\left(3z+a+1\right)}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 1-z.

$$3z-2+6-6z=5\left(c-3z\right)-4a$$

Add -2 and 6 to get 4.

$$3z+4-6z=5\left(c-3z\right)-4a$$

Combine 3z and -6z to get -3z.

$$-3z+4=5\left(c-3z\right)-4a$$

Use the distributive property to multiply 5 by c-3z.

$$-3z+4=5c-15z-4a$$

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

$$5c-15z-4a=-3z+4$$

Add 15z to both sides.

$$5c-4a=-3z+4+15z$$

Combine -3z and 15z to get 12z.

$$5c-4a=12z+4$$

Add 4a to both sides.

$$5c=12z+4+4a$$

The equation is in standard form.

$$5c=12z+4a+4$$

Divide both sides by 5.

$$\frac{5c}{5}=\frac{12z+4a+4}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$c=\frac{12z+4a+4}{5}$$