Solve x^2+2x(4-3a)=48a

$$x ^ { 2 } + 2 x ( 4 - 3 a ) = 48 a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{x}{6}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by 4-3a.

$$x^{2}+8x-6ax=48a$$

Subtract 48a from both sides.

$$x^{2}+8x-6ax-48a=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$8x-6ax-48a=-x^{2}$$

Subtract 8x from both sides.

$$-6ax-48a=-x^{2}-8x$$

Combine all terms containing a.

$$\left(-6x-48\right)a=-x^{2}-8x$$

Divide both sides by -6x-48.

$$\frac{\left(-6x-48\right)a}{-6x-48}=-\frac{x\left(x+8\right)}{-6x-48}$$

Dividing by -6x-48 undoes the multiplication by -6x-48.

$$a=-\frac{x\left(x+8\right)}{-6x-48}$$

Divide -x\left(8+x\right) by -6x-48.

$$a=\frac{x}{6}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{x}{6}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by 4-3a.

$$x^{2}+8x-6ax=48a$$

Subtract 48a from both sides.

$$x^{2}+8x-6ax-48a=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$8x-6ax-48a=-x^{2}$$

Subtract 8x from both sides.

$$-6ax-48a=-x^{2}-8x$$

Combine all terms containing a.

$$\left(-6x-48\right)a=-x^{2}-8x$$

Divide both sides by -6x-48.

$$\frac{\left(-6x-48\right)a}{-6x-48}=-\frac{x\left(x+8\right)}{-6x-48}$$

Dividing by -6x-48 undoes the multiplication by -6x-48.

$$a=-\frac{x\left(x+8\right)}{-6x-48}$$

Divide -x\left(8+x\right) by -6x-48.

$$a=\frac{x}{6}$$

Solve for x

$$x=6a$$

$$x=-8$$