Solve 3x-A(A^3/9+A^2)=9-A^2

$$3 x - A ( \frac { A ^ { 3 } } { 9 + A ^ { 2 } } ) = 9 - A ^ { 2 }$$

Solve for x (complex solution)

$$x=\frac{27}{A^{2}+9}$$

$$A\neq -3i\text{ and }A\neq 3i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(A-3i\right)\left(A+3i\right).

$$3x\left(A-3i\right)\left(A+3i\right)-AA^{3}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3x\left(A-3i\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply 3x by A-3i.

$$\left(3xA-9ix\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply 3xA-9ix by A+3i and combine like terms.

$$3xA^{2}+27x-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply A-3i by A+3i and combine like terms.

$$3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply A^{2}+9 by 9.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply -A^{2} by A-3i.

$$3xA^{2}+27x-A^{4}=9A^{2}+81+\left(-A^{3}+3iA^{2}\right)\left(A+3i\right)$$

Use the distributive property to multiply -A^{3}+3iA^{2} by A+3i and combine like terms.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

Combine 9A^{2} and -9A^{2} to get 0.

$$3xA^{2}+27x-A^{4}=81-A^{4}$$

Add A^{4} to both sides.

$$3xA^{2}+27x=81-A^{4}+A^{4}$$

Combine -A^{4} and A^{4} to get 0.

$$3xA^{2}+27x=81$$

Combine all terms containing x.

$$\left(3A^{2}+27\right)x=81$$

Divide both sides by 3A^{2}+27.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}$$

Dividing by 3A^{2}+27 undoes the multiplication by 3A^{2}+27.

$$x=\frac{81}{3A^{2}+27}$$

Divide 81 by 3A^{2}+27.

$$x=\frac{27}{A^{2}+9}$$

Solve for x

$$x=\frac{27}{A^{2}+9}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A^{2}+9.

$$3x\left(A^{2}+9\right)-AA^{3}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3x\left(A^{2}+9\right)-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

Use the distributive property to multiply 3x by A^{2}+9.

$$3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

Use the distributive property to multiply A^{2}+9 by 9.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A^{2}+9\right)$$

Use the distributive property to multiply -A^{2} by A^{2}+9.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

Combine 9A^{2} and -9A^{2} to get 0.

$$3xA^{2}+27x-A^{4}=81-A^{4}$$

Add A^{4} to both sides.

$$3xA^{2}+27x=81-A^{4}+A^{4}$$

Combine -A^{4} and A^{4} to get 0.

$$3xA^{2}+27x=81$$

Combine all terms containing x.

$$\left(3A^{2}+27\right)x=81$$

Divide both sides by 3A^{2}+27.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}$$

Dividing by 3A^{2}+27 undoes the multiplication by 3A^{2}+27.

$$x=\frac{81}{3A^{2}+27}$$

Divide 81 by 3A^{2}+27.

$$x=\frac{27}{A^{2}+9}$$

Solve for A (complex solution)

$$A=-3\sqrt{-1+\frac{3}{x}}$$

$$A=3\sqrt{-1+\frac{3}{x}}\text{, }x\neq 0$$

Solve for A

$$A=3\sqrt{-1+\frac{3}{x}}$$

$$A=-3\sqrt{-1+\frac{3}{x}}\text{, }x>0\text{ and }x\leq 3$$