Solve 27(x-6)+26(x+7)-33z=0

$$27 ( x - 6 ) + 26 ( x + 7 ) - 33 z = 0$$

Solve for x

$$x=\frac{33z-20}{53}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 27 by x-6.

$$27x-162+26\left(x+7\right)-33z=0$$

Use the distributive property to multiply 26 by x+7.

$$27x-162+26x+182-33z=0$$

Combine 27x and 26x to get 53x.

$$53x-162+182-33z=0$$

Add -162 and 182 to get 20.

$$53x+20-33z=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$53x-33z=-20$$

Add 33z to both sides.

$$53x=-20+33z$$

The equation is in standard form.

$$53x=33z-20$$

Divide both sides by 53.

$$\frac{53x}{53}=\frac{33z-20}{53}$$

Dividing by 53 undoes the multiplication by 53.

$$x=\frac{33z-20}{53}$$

Solve for z

$$z=\frac{53x+20}{33}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 27 by x-6.

$$27x-162+26\left(x+7\right)-33z=0$$

Use the distributive property to multiply 26 by x+7.

$$27x-162+26x+182-33z=0$$

Combine 27x and 26x to get 53x.

$$53x-162+182-33z=0$$

Add -162 and 182 to get 20.

$$53x+20-33z=0$$

Subtract 53x from both sides. Anything subtracted from zero gives its negation.

$$20-33z=-53x$$

Subtract 20 from both sides.

$$-33z=-53x-20$$

Divide both sides by -33.

$$\frac{-33z}{-33}=\frac{-53x-20}{-33}$$

Dividing by -33 undoes the multiplication by -33.

$$z=\frac{-53x-20}{-33}$$

Divide -53x-20 by -33.

$$z=\frac{53x+20}{33}$$