Solve x+6(-z+102/25)-z=27

$$x + 6 ( \frac { - z + 102 } { 25 } ) - z = 27$$

Solve for x

$$x=\frac{31z+63}{25}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 25.

$$25x+6\left(-z+102\right)-25z=675$$

Use the distributive property to multiply 6 by -z+102.

$$25x+6\left(-z\right)+612-25z=675$$

Subtract 6\left(-z\right) from both sides.

$$25x+612-25z=675-6\left(-z\right)$$

Subtract 612 from both sides.

$$25x-25z=675-6\left(-z\right)-612$$

Add 25z to both sides.

$$25x=675-6\left(-z\right)-612+25z$$

Multiply -1 and 6 to get -6.

$$25x=675-6\left(-1\right)z-612+25z$$

Multiply -6 and -1 to get 6.

$$25x=675+6z-612+25z$$

Subtract 612 from 675 to get 63.

$$25x=63+6z+25z$$

Combine 6z and 25z to get 31z.

$$25x=63+31z$$

The equation is in standard form.

$$25x=31z+63$$

Divide both sides by 25.

$$\frac{25x}{25}=\frac{31z+63}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$x=\frac{31z+63}{25}$$

Solve for z

$$z=\frac{25x-63}{31}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 25.

$$25x+6\left(-z+102\right)-25z=675$$

Use the distributive property to multiply 6 by -z+102.

$$25x+6\left(-z\right)+612-25z=675$$

Subtract 25x from both sides.

$$6\left(-z\right)+612-25z=675-25x$$

Subtract 612 from both sides.

$$6\left(-z\right)-25z=675-25x-612$$

Subtract 612 from 675 to get 63.

$$6\left(-z\right)-25z=63-25x$$

Multiply 6 and -1 to get -6.

$$-6z-25z=63-25x$$

Combine -6z and -25z to get -31z.

$$-31z=63-25x$$

Divide both sides by -31.

$$\frac{-31z}{-31}=\frac{63-25x}{-31}$$

Dividing by -31 undoes the multiplication by -31.

$$z=\frac{63-25x}{-31}$$

Divide 63-25x by -31.

$$z=\frac{25x-63}{31}$$