Solve y=2x+5/3n-7[x]

$$y = \frac { 2 x + 5 } { 3 n - 7 } [ x ]$$

Solve for n

$$\left\{\begin{matrix}n=\frac{2x^{2}+5x+7y}{3y}\text{, }&x\neq -\frac{5}{2}\text{ and }x\neq 0\text{ and }y\neq 0\\n\neq \frac{7}{3}\text{, }&\left(x=0\text{ or }x=-\frac{5}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to \frac{7}{3} since division by zero is not defined. Multiply both sides of the equation by 3n-7.

$$y\left(3n-7\right)=\left(2x+5\right)x$$

Use the distributive property to multiply y by 3n-7.

$$3yn-7y=\left(2x+5\right)x$$

Use the distributive property to multiply 2x+5 by x.

$$3yn-7y=2x^{2}+5x$$

Add 7y to both sides.

$$3yn=2x^{2}+5x+7y$$

Divide both sides by 3y.

$$\frac{3yn}{3y}=\frac{2x^{2}+5x+7y}{3y}$$

Dividing by 3y undoes the multiplication by 3y.

$$n=\frac{2x^{2}+5x+7y}{3y}$$

Variable n cannot be equal to \frac{7}{3}.

$$n=\frac{2x^{2}+5x+7y}{3y}\text{, }n\neq \frac{7}{3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{24ny-56y+25}-5}{4}$$

$$x=\frac{-\sqrt{24ny-56y+25}-5}{4}\text{, }n\neq \frac{7}{3}$$

Solve for x

$$x=\frac{\sqrt{24ny-56y+25}-5}{4}$$

$$x=\frac{-\sqrt{24ny-56y+25}-5}{4}\text{, }\left(n>\frac{7}{3}\text{ or }y\leq -\frac{25}{24n-56}\right)\text{ and }\left(n<\frac{7}{3}\text{ or }y\geq -\frac{25}{24n-56}\right)\text{ and }n\neq \frac{7}{3}$$