Solve 5/21-2/4+3-4z-3/14=4z-3(z-2)/7

$$\frac { 5 } { 21 } - \frac { 2 } { 4 } + 3 - \frac { 4 z - 3 } { 14 } = 4 z - \frac { 3 ( z - 2 ) } { 7 }$$

Solve for z

$$z=\frac{44}{81}\approx 0.543209877$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 84, the least common multiple of 21,4,14,7.

$$20-21\times 2+252-6\left(4z-3\right)=336z-12\times 3\left(z-2\right)$$

Multiply -21 and 2 to get -42.

$$20-42+252-6\left(4z-3\right)=336z-12\times 3\left(z-2\right)$$

Subtract 42 from 20 to get -22.

$$-22+252-6\left(4z-3\right)=336z-12\times 3\left(z-2\right)$$

Add -22 and 252 to get 230.

$$230-6\left(4z-3\right)=336z-12\times 3\left(z-2\right)$$

Use the distributive property to multiply -6 by 4z-3.

$$230-24z+18=336z-12\times 3\left(z-2\right)$$

Add 230 and 18 to get 248.

$$248-24z=336z-12\times 3\left(z-2\right)$$

Multiply -12 and 3 to get -36.

$$248-24z=336z-36\left(z-2\right)$$

Use the distributive property to multiply -36 by z-2.

$$248-24z=336z-36z+72$$

Combine 336z and -36z to get 300z.

$$248-24z=300z+72$$

Subtract 300z from both sides.

$$248-24z-300z=72$$

Combine -24z and -300z to get -324z.

$$248-324z=72$$

Subtract 248 from both sides.

$$-324z=72-248$$

Subtract 248 from 72 to get -176.

$$-324z=-176$$

Divide both sides by -324.

$$z=\frac{-176}{-324}$$

Reduce the fraction \frac{-176}{-324} to lowest terms by extracting and canceling out -4.

$$z=\frac{44}{81}$$