Solve for F (complex solution)
\left\{\begin{matrix}F=-\frac{-2x^{2}+px+5x-2p-8}{x+2}\text{, }&x\neq -2\\F\in \mathrm{C}\text{, }&x=-2\text{ and }p=-\frac{13}{2}\end{matrix}\right.
Solve for p (complex solution)
\left\{\begin{matrix}p=-\frac{-2x^{2}+Fx+5x+2F-8}{x-2}\text{, }&x\neq 2\\p\in \mathrm{C}\text{, }&x=2\text{ and }F=\frac{3}{2}\end{matrix}\right.
Solve for F
\left\{\begin{matrix}F=-\frac{-2x^{2}+px+5x-2p-8}{x+2}\text{, }&x\neq -2\\F\in \mathrm{R}\text{, }&x=-2\text{ and }p=-\frac{13}{2}\end{matrix}\right.
Solve for p
\left\{\begin{matrix}p=-\frac{-2x^{2}+Fx+5x+2F-8}{x-2}\text{, }&x\neq 2\\p\in \mathrm{R}\text{, }&x=2\text{ and }F=\frac{3}{2}\end{matrix}\right.
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px-2p+F\left(x+2\right)=2x^{2}-5x+8
Use the distributive property to multiply p by x-2.
px-2p+Fx+2F=2x^{2}-5x+8
Use the distributive property to multiply F by x+2.
-2p+Fx+2F=2x^{2}-5x+8-px
Subtract px from both sides.
Fx+2F=2x^{2}-5x+8-px+2p
Add 2p to both sides.
\left(x+2\right)F=2x^{2}-5x+8-px+2p
Combine all terms containing F.
\left(x+2\right)F=2x^{2}-px-5x+2p+8
The equation is in standard form.
\frac{\left(x+2\right)F}{x+2}=\frac{2x^{2}-px-5x+2p+8}{x+2}
Divide both sides by x+2.
F=\frac{2x^{2}-px-5x+2p+8}{x+2}
Dividing by x+2 undoes the multiplication by x+2.
px-2p+F\left(x+2\right)=2x^{2}-5x+8
Use the distributive property to multiply p by x-2.
px-2p+Fx+2F=2x^{2}-5x+8
Use the distributive property to multiply F by x+2.
px-2p+2F=2x^{2}-5x+8-Fx
Subtract Fx from both sides.
px-2p=2x^{2}-5x+8-Fx-2F
Subtract 2F from both sides.
\left(x-2\right)p=2x^{2}-5x+8-Fx-2F
Combine all terms containing p.
\left(x-2\right)p=2x^{2}-Fx-5x-2F+8
The equation is in standard form.
\frac{\left(x-2\right)p}{x-2}=\frac{2x^{2}-Fx-5x-2F+8}{x-2}
Divide both sides by x-2.
p=\frac{2x^{2}-Fx-5x-2F+8}{x-2}
Dividing by x-2 undoes the multiplication by x-2.
px-2p+F\left(x+2\right)=2x^{2}-5x+8
Use the distributive property to multiply p by x-2.
px-2p+Fx+2F=2x^{2}-5x+8
Use the distributive property to multiply F by x+2.
-2p+Fx+2F=2x^{2}-5x+8-px
Subtract px from both sides.
Fx+2F=2x^{2}-5x+8-px+2p
Add 2p to both sides.
\left(x+2\right)F=2x^{2}-5x+8-px+2p
Combine all terms containing F.
\left(x+2\right)F=2x^{2}-px-5x+2p+8
The equation is in standard form.
\frac{\left(x+2\right)F}{x+2}=\frac{2x^{2}-px-5x+2p+8}{x+2}
Divide both sides by x+2.
F=\frac{2x^{2}-px-5x+2p+8}{x+2}
Dividing by x+2 undoes the multiplication by x+2.
px-2p+F\left(x+2\right)=2x^{2}-5x+8
Use the distributive property to multiply p by x-2.
px-2p+Fx+2F=2x^{2}-5x+8
Use the distributive property to multiply F by x+2.
px-2p+2F=2x^{2}-5x+8-Fx
Subtract Fx from both sides.
px-2p=2x^{2}-5x+8-Fx-2F
Subtract 2F from both sides.
\left(x-2\right)p=2x^{2}-5x+8-Fx-2F
Combine all terms containing p.
\left(x-2\right)p=2x^{2}-Fx-5x-2F+8
The equation is in standard form.
\frac{\left(x-2\right)p}{x-2}=\frac{2x^{2}-Fx-5x-2F+8}{x-2}
Divide both sides by x-2.
p=\frac{2x^{2}-Fx-5x-2F+8}{x-2}
Dividing by x-2 undoes the multiplication by x-2.
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