Solve 9x=b(12-3x^2)

$$9 x = b ( 12 - 3 x ^ { 2 } )$$

Solve for b (complex solution)

$$b=-\frac{3x}{x^{2}-4}$$

$$x\neq -2\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by 12-3x^{2}.

$$9x=12b-3bx^{2}$$

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

$$12b-3bx^{2}=9x$$

Combine all terms containing b.

$$\left(12-3x^{2}\right)b=9x$$

Divide both sides by 12-3x^{2}.

$$\frac{\left(12-3x^{2}\right)b}{12-3x^{2}}=\frac{9x}{12-3x^{2}}$$

Dividing by 12-3x^{2} undoes the multiplication by 12-3x^{2}.

$$b=\frac{9x}{12-3x^{2}}$$

Divide 9x by 12-3x^{2}.

$$b=\frac{3x}{4-x^{2}}$$

Solve for b

$$b=-\frac{3x}{x^{2}-4}$$

$$|x|\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by 12-3x^{2}.

$$9x=12b-3bx^{2}$$

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

$$12b-3bx^{2}=9x$$

Combine all terms containing b.

$$\left(12-3x^{2}\right)b=9x$$

Divide both sides by 12-3x^{2}.

$$\frac{\left(12-3x^{2}\right)b}{12-3x^{2}}=\frac{9x}{12-3x^{2}}$$

Dividing by 12-3x^{2} undoes the multiplication by 12-3x^{2}.

$$b=\frac{9x}{12-3x^{2}}$$

Divide 9x by 12-3x^{2}.

$$b=\frac{3x}{4-x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{16b^{2}+9}-3}{2b}\text{; }x=-\frac{\sqrt{16b^{2}+9}+3}{2b}\text{, }&b\neq 0\\x=0\text{, }&b=0\end{matrix}\right.$$