Solve 1/4ax^3+9bx-6c=0

$$\frac { 1 } { 4 } a x ^ { 3 } + 9 b x - 6 c = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{12\left(3bx-2c\right)}{x^{3}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 9bx from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{4}ax^{3}-6c=-9bx$$

Add 6c to both sides.

$$\frac{1}{4}ax^{3}=-9bx+6c$$

The equation is in standard form.

$$\frac{x^{3}}{4}a=6c-9bx$$

Divide both sides by \frac{1}{4}x^{3}.

$$\frac{4\times \frac{x^{3}}{4}a}{x^{3}}=\frac{4\left(6c-9bx\right)}{x^{3}}$$

Dividing by \frac{1}{4}x^{3} undoes the multiplication by \frac{1}{4}x^{3}.

$$a=\frac{4\left(6c-9bx\right)}{x^{3}}$$

Divide -9bx+6c by \frac{1}{4}x^{3}.

$$a=\frac{12\left(2c-3bx\right)}{x^{3}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ax^{2}}{36}+\frac{2c}{3x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{1}{4}ax^{3} from both sides. Anything subtracted from zero gives its negation.

$$9bx-6c=-\frac{1}{4}ax^{3}$$

Add 6c to both sides.

$$9bx=-\frac{1}{4}ax^{3}+6c$$

The equation is in standard form.

$$9xb=-\frac{ax^{3}}{4}+6c$$

Divide both sides by 9x.

$$\frac{9xb}{9x}=\frac{-\frac{ax^{3}}{4}+6c}{9x}$$

Dividing by 9x undoes the multiplication by 9x.

$$b=\frac{-\frac{ax^{3}}{4}+6c}{9x}$$

Divide -\frac{ax^{3}}{4}+6c by 9x.

$$b=-\frac{ax^{2}}{36}+\frac{2c}{3x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{12\left(3bx-2c\right)}{x^{3}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 9bx from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{4}ax^{3}-6c=-9bx$$

Add 6c to both sides.

$$\frac{1}{4}ax^{3}=-9bx+6c$$

The equation is in standard form.

$$\frac{x^{3}}{4}a=6c-9bx$$

Divide both sides by \frac{1}{4}x^{3}.

$$\frac{4\times \frac{x^{3}}{4}a}{x^{3}}=\frac{4\left(6c-9bx\right)}{x^{3}}$$

Dividing by \frac{1}{4}x^{3} undoes the multiplication by \frac{1}{4}x^{3}.

$$a=\frac{4\left(6c-9bx\right)}{x^{3}}$$

Divide -9bx+6c by \frac{1}{4}x^{3}.

$$a=\frac{12\left(2c-3bx\right)}{x^{3}}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax^{2}}{36}+\frac{2c}{3x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{1}{4}ax^{3} from both sides. Anything subtracted from zero gives its negation.

$$9bx-6c=-\frac{1}{4}ax^{3}$$

Add 6c to both sides.

$$9bx=-\frac{1}{4}ax^{3}+6c$$

The equation is in standard form.

$$9xb=-\frac{ax^{3}}{4}+6c$$

Divide both sides by 9x.

$$\frac{9xb}{9x}=\frac{-\frac{ax^{3}}{4}+6c}{9x}$$

Dividing by 9x undoes the multiplication by 9x.

$$b=\frac{-\frac{ax^{3}}{4}+6c}{9x}$$

Divide -\frac{ax^{3}}{4}+6c by 9x.

$$b=-\frac{ax^{2}}{36}+\frac{2c}{3x}$$