Solve 7g5*(2v-7)=4v-17du

$$7 g 5 \cdot ( 2 v - 7 ) = 4 v - 17 d u$$

Solve for d

$$\left\{\begin{matrix}d=\frac{49g_{5}+4v-14g_{5}v}{17u}\text{, }&u\neq 0\\d\in \mathrm{R}\text{, }&g_{5}=-\frac{4v}{7\left(7-2v\right)}\text{ and }v\neq \frac{7}{2}\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7g_{5} by 2v-7.

$$14g_{5}v-49g_{5}=4v-17du$$

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

$$4v-17du=14g_{5}v-49g_{5}$$

Subtract 4v from both sides.

$$-17du=14g_{5}v-49g_{5}-4v$$

The equation is in standard form.

$$\left(-17u\right)d=14g_{5}v-4v-49g_{5}$$

Divide both sides by -17u.

$$\frac{\left(-17u\right)d}{-17u}=\frac{14g_{5}v-4v-49g_{5}}{-17u}$$

Dividing by -17u undoes the multiplication by -17u.

$$d=\frac{14g_{5}v-4v-49g_{5}}{-17u}$$

Divide 14g_{5}v-49g_{5}-4v by -17u.

$$d=-\frac{14g_{5}v-4v-49g_{5}}{17u}$$

Solve for g_5

$$\left\{\begin{matrix}g_{5}=-\frac{17du-4v}{7\left(2v-7\right)}\text{, }&v\neq \frac{7}{2}\\g_{5}\in \mathrm{R}\text{, }&v=\frac{7}{2}\text{ and }d=\frac{14}{17u}\text{ and }u\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7g_{5} by 2v-7.

$$14g_{5}v-49g_{5}=4v-17du$$

Combine all terms containing g_{5}.

$$\left(14v-49\right)g_{5}=4v-17du$$

Divide both sides by -49+14v.

$$\frac{\left(14v-49\right)g_{5}}{14v-49}=\frac{4v-17du}{14v-49}$$

Dividing by -49+14v undoes the multiplication by -49+14v.

$$g_{5}=\frac{4v-17du}{14v-49}$$

Divide 4v-17du by -49+14v.

$$g_{5}=\frac{4v-17du}{7\left(2v-7\right)}$$