Solve for m (complex solution)
\left\{\begin{matrix}m=-\frac{5x+n+3}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=-3\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=-\frac{5x+n+3}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=-3\end{matrix}\right.
Solve for n
n=-\left(mx+5x+3\right)
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2x^{2}-5x-3=2x^{2}+mx+n
Use the distributive property to multiply x-3 by 2x+1 and combine like terms.
2x^{2}+mx+n=2x^{2}-5x-3
Swap sides so that all variable terms are on the left hand side.
mx+n=2x^{2}-5x-3-2x^{2}
Subtract 2x^{2} from both sides.
mx+n=-5x-3
Combine 2x^{2} and -2x^{2} to get 0.
mx=-5x-3-n
Subtract n from both sides.
xm=-5x-n-3
The equation is in standard form.
\frac{xm}{x}=\frac{-5x-n-3}{x}
Divide both sides by x.
m=\frac{-5x-n-3}{x}
Dividing by x undoes the multiplication by x.
m=-\frac{5x+n+3}{x}
Divide -5x-3-n by x.
2x^{2}-5x-3=2x^{2}+mx+n
Use the distributive property to multiply x-3 by 2x+1 and combine like terms.
2x^{2}+mx+n=2x^{2}-5x-3
Swap sides so that all variable terms are on the left hand side.
mx+n=2x^{2}-5x-3-2x^{2}
Subtract 2x^{2} from both sides.
mx+n=-5x-3
Combine 2x^{2} and -2x^{2} to get 0.
mx=-5x-3-n
Subtract n from both sides.
xm=-5x-n-3
The equation is in standard form.
\frac{xm}{x}=\frac{-5x-n-3}{x}
Divide both sides by x.
m=\frac{-5x-n-3}{x}
Dividing by x undoes the multiplication by x.
m=-\frac{5x+n+3}{x}
Divide -5x-3-n by x.
2x^{2}-5x-3=2x^{2}+mx+n
Use the distributive property to multiply x-3 by 2x+1 and combine like terms.
2x^{2}+mx+n=2x^{2}-5x-3
Swap sides so that all variable terms are on the left hand side.
mx+n=2x^{2}-5x-3-2x^{2}
Subtract 2x^{2} from both sides.
mx+n=-5x-3
Combine 2x^{2} and -2x^{2} to get 0.
n=-5x-3-mx
Subtract mx from both sides.
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