Solve f(x)dx=3x^2-6ax+5

$$f ( x ) d x = 3 x ^ { 2 } - 6 a x + 5$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=-\frac{-3x^{2}+6ax-5}{fx^{2}}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{C}\text{, }&a=\frac{x}{2}+\frac{5}{6x}\text{ and }x\neq 0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx^{2}d=3x^{2}-6ax+5$$

Divide both sides by fx^{2}.

$$\frac{fx^{2}d}{fx^{2}}=\frac{3x^{2}-6ax+5}{fx^{2}}$$

Dividing by fx^{2} undoes the multiplication by fx^{2}.

$$d=\frac{3x^{2}-6ax+5}{fx^{2}}$$

Solve for a

$$a=-\frac{dfx}{6}+\frac{x}{2}+\frac{5}{6x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$fx^{2}d=3x^{2}-6ax+5$$

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

$$3x^{2}-6ax+5=fx^{2}d$$

Subtract 3x^{2} from both sides.

$$-6ax+5=fx^{2}d-3x^{2}$$

Subtract 5 from both sides.

$$-6ax=fx^{2}d-3x^{2}-5$$

The equation is in standard form.

$$\left(-6x\right)a=dfx^{2}-3x^{2}-5$$

Divide both sides by -6x.

$$\frac{\left(-6x\right)a}{-6x}=\frac{dfx^{2}-3x^{2}-5}{-6x}$$

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

$$a=\frac{dfx^{2}-3x^{2}-5}{-6x}$$

Divide fx^{2}d-3x^{2}-5 by -6x.

$$a=-\frac{dfx}{6}+\frac{x}{2}+\frac{5}{6x}$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{-3x^{2}+6ax-5}{fx^{2}}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{R}\text{, }&a=\frac{x}{2}+\frac{5}{6x}\text{ and }x\neq 0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx^{2}d=3x^{2}-6ax+5$$

Divide both sides by fx^{2}.

$$\frac{fx^{2}d}{fx^{2}}=\frac{3x^{2}-6ax+5}{fx^{2}}$$

Dividing by fx^{2} undoes the multiplication by fx^{2}.

$$d=\frac{3x^{2}-6ax+5}{fx^{2}}$$