Solve (14+[4x(28+z:6)-5]:5=37

$$( 14 + [ 4 x ( 28 + z : 6 ) - 5 ] : 5 = 37$$

Solve for x

$$x=\frac{180}{z+168}$$

$$z\neq -168$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$70+4x\left(28+\frac{z}{6}\right)-5=185$$

Use the distributive property to multiply 4x by 28+\frac{z}{6}.

$$70+112x+4x\times \frac{z}{6}-5=185$$

Express 4\times \frac{z}{6} as a single fraction.

$$70+112x+\frac{4z}{6}x-5=185$$

Divide 4z by 6 to get \frac{2}{3}z.

$$70+112x+\frac{2}{3}zx-5=185$$

Subtract 5 from 70 to get 65.

$$65+112x+\frac{2}{3}zx=185$$

Subtract 65 from both sides.

$$112x+\frac{2}{3}zx=185-65$$

Subtract 65 from 185 to get 120.

$$112x+\frac{2}{3}zx=120$$

Combine all terms containing x.

$$\left(112+\frac{2}{3}z\right)x=120$$

The equation is in standard form.

$$\left(\frac{2z}{3}+112\right)x=120$$

Divide both sides by 112+\frac{2}{3}z.

$$\frac{\left(\frac{2z}{3}+112\right)x}{\frac{2z}{3}+112}=\frac{120}{\frac{2z}{3}+112}$$

Dividing by 112+\frac{2}{3}z undoes the multiplication by 112+\frac{2}{3}z.

$$x=\frac{120}{\frac{2z}{3}+112}$$

Divide 120 by 112+\frac{2}{3}z.

$$x=\frac{180}{z+168}$$

Solve for z

$$z=-168+\frac{180}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$70+4x\left(28+\frac{z}{6}\right)-5=185$$

Use the distributive property to multiply 4x by 28+\frac{z}{6}.

$$70+112x+4x\times \frac{z}{6}-5=185$$

Express 4\times \frac{z}{6} as a single fraction.

$$70+112x+\frac{4z}{6}x-5=185$$

Divide 4z by 6 to get \frac{2}{3}z.

$$70+112x+\frac{2}{3}zx-5=185$$

Subtract 5 from 70 to get 65.

$$65+112x+\frac{2}{3}zx=185$$

Subtract 65 from both sides.

$$112x+\frac{2}{3}zx=185-65$$

Subtract 65 from 185 to get 120.

$$112x+\frac{2}{3}zx=120$$

Subtract 112x from both sides.

$$\frac{2}{3}zx=120-112x$$

The equation is in standard form.

$$\frac{2x}{3}z=120-112x$$

Divide both sides by \frac{2}{3}x.

$$\frac{3\times \frac{2x}{3}z}{2x}=\frac{3\left(120-112x\right)}{2x}$$

Dividing by \frac{2}{3}x undoes the multiplication by \frac{2}{3}x.

$$z=\frac{3\left(120-112x\right)}{2x}$$

Divide 120-112x by \frac{2}{3}x.

$$z=-168+\frac{180}{x}$$