Solve 9(aq^2+aq^4)=7aq^3+14aq^5

$$9 ( a q ^ { 2 } + a q ^ { 4 } ) = 7 a q ^ { 3 } + 14 a q ^ { 5 }$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&q=0\text{ or }q=\sqrt[3]{\frac{\sqrt{981753}}{3528}+\frac{381}{1372}}+\sqrt[3]{-\frac{\sqrt{981753}}{3528}+\frac{381}{1372}}+\frac{3}{14}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9 by aq^{2}+aq^{4}.

$$9aq^{2}+9aq^{4}=7aq^{3}+14aq^{5}$$

Subtract 7aq^{3} from both sides.

$$9aq^{2}+9aq^{4}-7aq^{3}=14aq^{5}$$

Subtract 14aq^{5} from both sides.

$$9aq^{2}+9aq^{4}-7aq^{3}-14aq^{5}=0$$

Combine all terms containing a.

$$\left(9q^{2}+9q^{4}-7q^{3}-14q^{5}\right)a=0$$

The equation is in standard form.

$$\left(9q^{2}-7q^{3}+9q^{4}-14q^{5}\right)a=0$$

Divide 0 by 9q^{2}+9q^{4}-7q^{3}-14q^{5}.

$$a=0$$

Solve for q

$$\left\{\begin{matrix}\\q=0\text{; }q=\frac{9^{\frac{2}{3}}\left(\sqrt[3]{7\sqrt{981753}+6858}+\sqrt[3]{6858-7\sqrt{981753}}+3\sqrt[3]{9}\right)}{126}\text{, }&\text{unconditionally}\\q\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$