Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{6x+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }c=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{6x+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right.
Solve for c
c=-x\left(ax+6\right)
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ax^{2}+c=-6x
Subtract 6x from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-6x-c
Subtract c from both sides.
x^{2}a=-6x-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-6x-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-6x-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{6x+c}{x^{2}}
Divide -6x-c by x^{2}.
ax^{2}+c=-6x
Subtract 6x from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-6x-c
Subtract c from both sides.
x^{2}a=-6x-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-6x-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-6x-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{6x+c}{x^{2}}
Divide -6x-c by x^{2}.
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