Solve 6*x-(x+5)operatorname{npn}x=-3

$$6 \cdot x - ( x + 5 ) \operatorname { npn } x = - 3$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}\text{, }&n\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\p\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply n and n to get n^{2}.

$$6x-\left(x+5\right)n^{2}px=-3$$

Use the distributive property to multiply x+5 by n^{2}.

$$6x-\left(xn^{2}+5n^{2}\right)px=-3$$

Use the distributive property to multiply xn^{2}+5n^{2} by p.

$$6x-\left(xn^{2}p+5n^{2}p\right)x=-3$$

Use the distributive property to multiply xn^{2}p+5n^{2}p by x.

$$6x-\left(n^{2}px^{2}+5n^{2}px\right)=-3$$

To find the opposite of n^{2}px^{2}+5n^{2}px, find the opposite of each term.

$$6x-n^{2}px^{2}-5n^{2}px=-3$$

Subtract 6x from both sides.

$$-n^{2}px^{2}-5n^{2}px=-3-6x$$

Combine all terms containing p.

$$\left(-n^{2}x^{2}-5n^{2}x\right)p=-3-6x$$

The equation is in standard form.

$$\left(-n^{2}x^{2}-5xn^{2}\right)p=-6x-3$$

Divide both sides by -5xn^{2}-x^{2}n^{2}.

$$\frac{\left(-n^{2}x^{2}-5xn^{2}\right)p}{-n^{2}x^{2}-5xn^{2}}=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Dividing by -5xn^{2}-x^{2}n^{2} undoes the multiplication by -5xn^{2}-x^{2}n^{2}.

$$p=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Divide -3-6x by -5xn^{2}-x^{2}n^{2}.

$$p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}\text{, }&n\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\p\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply n and n to get n^{2}.

$$6x-\left(x+5\right)n^{2}px=-3$$

Use the distributive property to multiply x+5 by n^{2}.

$$6x-\left(xn^{2}+5n^{2}\right)px=-3$$

Use the distributive property to multiply xn^{2}+5n^{2} by p.

$$6x-\left(xn^{2}p+5n^{2}p\right)x=-3$$

Use the distributive property to multiply xn^{2}p+5n^{2}p by x.

$$6x-\left(n^{2}px^{2}+5n^{2}px\right)=-3$$

To find the opposite of n^{2}px^{2}+5n^{2}px, find the opposite of each term.

$$6x-n^{2}px^{2}-5n^{2}px=-3$$

Subtract 6x from both sides.

$$-n^{2}px^{2}-5n^{2}px=-3-6x$$

Combine all terms containing p.

$$\left(-n^{2}x^{2}-5n^{2}x\right)p=-3-6x$$

The equation is in standard form.

$$\left(-n^{2}x^{2}-5xn^{2}\right)p=-6x-3$$

Divide both sides by -5xn^{2}-x^{2}n^{2}.

$$\frac{\left(-n^{2}x^{2}-5xn^{2}\right)p}{-n^{2}x^{2}-5xn^{2}}=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Dividing by -5xn^{2}-x^{2}n^{2} undoes the multiplication by -5xn^{2}-x^{2}n^{2}.

$$p=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Divide -6x-3 by -5xn^{2}-x^{2}n^{2}.

$$p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-ip^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}\sqrt{-6x-3}\text{; }n=ip^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}\sqrt{-6x-3}\text{, }&p\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\n\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }p=0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\sqrt{\frac{3\left(2x+1\right)}{px\left(x+5\right)}}\text{; }n=-\sqrt{\frac{3\left(2x+1\right)}{px\left(x+5\right)}}\text{, }&\left(x<-5\text{ and }p<0\right)\text{ or }\left(p>0\text{ and }x>0\right)\text{ or }\left(x\geq -\frac{1}{2}\text{ and }x<0\text{ and }p<0\right)\text{ or }\left(x\leq -\frac{1}{2}\text{ and }p>0\text{ and }x>-5\right)\\n\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }p=0\end{matrix}\right.$$