Solve for k (complex solution)
\left\{\begin{matrix}k=\frac{a-12x}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
Solve for a
a=x\left(kx+12\right)
Solve for k
\left\{\begin{matrix}k=\frac{a-12x}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
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kx^{2}-a=-12x
Subtract 12x from both sides. Anything subtracted from zero gives its negation.
kx^{2}=-12x+a
Add a to both sides.
x^{2}k=a-12x
The equation is in standard form.
\frac{x^{2}k}{x^{2}}=\frac{a-12x}{x^{2}}
Divide both sides by x^{2}.
k=\frac{a-12x}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
12x-a=-kx^{2}
Subtract kx^{2} from both sides. Anything subtracted from zero gives its negation.
-a=-kx^{2}-12x
Subtract 12x from both sides.
\frac{-a}{-1}=-\frac{x\left(kx+12\right)}{-1}
Divide both sides by -1.
a=-\frac{x\left(kx+12\right)}{-1}
Dividing by -1 undoes the multiplication by -1.
a=x\left(kx+12\right)
Divide -x\left(kx+12\right) by -1.
kx^{2}-a=-12x
Subtract 12x from both sides. Anything subtracted from zero gives its negation.
kx^{2}=-12x+a
Add a to both sides.
x^{2}k=a-12x
The equation is in standard form.
\frac{x^{2}k}{x^{2}}=\frac{a-12x}{x^{2}}
Divide both sides by x^{2}.
k=\frac{a-12x}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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