Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{3}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\frac{3}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x=\frac{3}{m}\text{, }&m\neq 0\end{matrix}\right.
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mx^{2}+mx-3x-3=0
Use the distributive property to multiply m-3 by x.
mx^{2}+mx-3=3x
Add 3x to both sides. Anything plus zero gives itself.
mx^{2}+mx=3x+3
Add 3 to both sides.
\left(x^{2}+x\right)m=3x+3
Combine all terms containing m.
\frac{\left(x^{2}+x\right)m}{x^{2}+x}=\frac{3x+3}{x^{2}+x}
Divide both sides by x^{2}+x.
m=\frac{3x+3}{x^{2}+x}
Dividing by x^{2}+x undoes the multiplication by x^{2}+x.
m=\frac{3}{x}
Divide 3+3x by x^{2}+x.
mx^{2}+mx-3x-3=0
Use the distributive property to multiply m-3 by x.
mx^{2}+mx-3=3x
Add 3x to both sides. Anything plus zero gives itself.
mx^{2}+mx=3x+3
Add 3 to both sides.
\left(x^{2}+x\right)m=3x+3
Combine all terms containing m.
\frac{\left(x^{2}+x\right)m}{x^{2}+x}=\frac{3x+3}{x^{2}+x}
Divide both sides by x^{2}+x.
m=\frac{3x+3}{x^{2}+x}
Dividing by x^{2}+x undoes the multiplication by x^{2}+x.
m=\frac{3}{x}
Divide 3+3x by x^{2}+x.
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Limits
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