Solve xdx=quadd(2x^2+3)

$$x d x = \quad d ( 2 x ^ { 2 } + 3 )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=-\sqrt{3}i\text{ or }x=\sqrt{3}i\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=d\left(2x^{2}+3\right)$$

Use the distributive property to multiply d by 2x^{2}+3.

$$x^{2}d=2dx^{2}+3d$$

Subtract 2dx^{2} from both sides.

$$x^{2}d-2dx^{2}=3d$$

Combine x^{2}d and -2dx^{2} to get -x^{2}d.

$$-x^{2}d=3d$$

Subtract 3d from both sides.

$$-x^{2}d-3d=0$$

Combine all terms containing d.

$$\left(-x^{2}-3\right)d=0$$

Divide 0 by -x^{2}-3.

$$d=0$$

Solve for d

$$d=0$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=d\left(2x^{2}+3\right)$$

Use the distributive property to multiply d by 2x^{2}+3.

$$x^{2}d=2dx^{2}+3d$$

Subtract 2dx^{2} from both sides.

$$x^{2}d-2dx^{2}=3d$$

Combine x^{2}d and -2dx^{2} to get -x^{2}d.

$$-x^{2}d=3d$$

Subtract 3d from both sides.

$$-x^{2}d-3d=0$$

Combine all terms containing d.

$$\left(-x^{2}-3\right)d=0$$

Divide 0 by -x^{2}-3.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\sqrt{3}i\text{; }x=\sqrt{3}i\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for x

$$x\in \mathrm{R}$$

$$d=0$$