Solve y=(1+8x)3x-4ax^2

$$y = ( 1 + 8 x ) 3 x - 4 a x ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=6-\frac{y}{4x^{2}}+\frac{3}{4x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+8x by 3.

$$y=\left(3+24x\right)x-4ax^{2}$$

Use the distributive property to multiply 3+24x by x.

$$y=3x+24x^{2}-4ax^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3x+24x^{2}-4ax^{2}=y$$

Subtract 3x from both sides.

$$24x^{2}-4ax^{2}=y-3x$$

Subtract 24x^{2} from both sides.

$$-4ax^{2}=y-3x-24x^{2}$$

The equation is in standard form.

$$\left(-4x^{2}\right)a=y-3x-24x^{2}$$

Divide both sides by -4x^{2}.

$$\frac{\left(-4x^{2}\right)a}{-4x^{2}}=\frac{y-3x-24x^{2}}{-4x^{2}}$$

Dividing by -4x^{2} undoes the multiplication by -4x^{2}.

$$a=\frac{y-3x-24x^{2}}{-4x^{2}}$$

Divide y-3x-24x^{2} by -4x^{2}.

$$a=6+\frac{3x-y}{4x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=6-\frac{y}{4x^{2}}+\frac{3}{4x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+8x by 3.

$$y=\left(3+24x\right)x-4ax^{2}$$

Use the distributive property to multiply 3+24x by x.

$$y=3x+24x^{2}-4ax^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3x+24x^{2}-4ax^{2}=y$$

Subtract 3x from both sides.

$$24x^{2}-4ax^{2}=y-3x$$

Subtract 24x^{2} from both sides.

$$-4ax^{2}=y-3x-24x^{2}$$

The equation is in standard form.

$$\left(-4x^{2}\right)a=y-3x-24x^{2}$$

Divide both sides by -4x^{2}.

$$\frac{\left(-4x^{2}\right)a}{-4x^{2}}=\frac{y-3x-24x^{2}}{-4x^{2}}$$

Dividing by -4x^{2} undoes the multiplication by -4x^{2}.

$$a=\frac{y-3x-24x^{2}}{-4x^{2}}$$

Divide y-3x-24x^{2} by -4x^{2}.

$$a=6+\frac{3x-y}{4x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{9+96y-16ay}+3}{8\left(a-6\right)}\text{; }x=\frac{-\sqrt{9+96y-16ay}+3}{8\left(a-6\right)}\text{, }&a\neq 6\\x=\frac{y}{3}\text{, }&a=6\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{9+96y-16ay}+3}{8\left(a-6\right)}\text{; }x=\frac{-\sqrt{9+96y-16ay}+3}{8\left(a-6\right)}\text{, }&\left(a<6\text{ or }y\leq -\frac{9}{96-16a}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq 6\right)\text{ and }\left(a>6\text{ or }\left(a\neq 6\text{ and }y\geq -\frac{9}{96-16a}\right)\right)\\x=\frac{y}{3}\text{, }&a=6\end{matrix}\right.$$