Solve ax^2+bx^2y=9x(2x-4xy)

$$a x ^ { 2 } + b x ^ { 2 } y = 9 x ( 2 x - 4 x y )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=18-36y-by\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9x by 2x-4xy.

$$ax^{2}+bx^{2}y=18x^{2}-36yx^{2}$$

Subtract bx^{2}y from both sides.

$$ax^{2}=18x^{2}-36yx^{2}-bx^{2}y$$

Reorder the terms.

$$ax^{2}=18x^{2}-byx^{2}-36yx^{2}$$

The equation is in standard form.

$$x^{2}a=18x^{2}-byx^{2}-36yx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{x^{2}\left(18-36y-by\right)}{x^{2}}$$

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

$$a=\frac{x^{2}\left(18-36y-by\right)}{x^{2}}$$

Divide \left(18-by-36y\right)x^{2} by x^{2}.

$$a=18-36y-by$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{36y+a-18}{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\left(a=18\text{ and }y=0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9x by 2x-4xy.

$$ax^{2}+bx^{2}y=18x^{2}-36yx^{2}$$

Subtract ax^{2} from both sides.

$$bx^{2}y=18x^{2}-36yx^{2}-ax^{2}$$

Reorder the terms.

$$byx^{2}=-ax^{2}+18x^{2}-36yx^{2}$$

The equation is in standard form.

$$yx^{2}b=18x^{2}-ax^{2}-36yx^{2}$$

Divide both sides by x^{2}y.

$$\frac{yx^{2}b}{yx^{2}}=\frac{\left(18-a-36y\right)x^{2}}{yx^{2}}$$

Dividing by x^{2}y undoes the multiplication by x^{2}y.

$$b=\frac{\left(18-a-36y\right)x^{2}}{yx^{2}}$$

Divide \left(18-a-36y\right)x^{2} by x^{2}y.

$$b=\frac{18-a-36y}{y}$$

Solve for a

$$\left\{\begin{matrix}\\a=18-36y-by\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9x by 2x-4xy.

$$ax^{2}+bx^{2}y=18x^{2}-36yx^{2}$$

Subtract bx^{2}y from both sides.

$$ax^{2}=18x^{2}-36yx^{2}-bx^{2}y$$

Reorder the terms.

$$ax^{2}=18x^{2}-byx^{2}-36yx^{2}$$

The equation is in standard form.

$$x^{2}a=18x^{2}-byx^{2}-36yx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{x^{2}\left(18-36y-by\right)}{x^{2}}$$

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

$$a=\frac{x^{2}\left(18-36y-by\right)}{x^{2}}$$

Divide \left(18-by-36y\right)x^{2} by x^{2}.

$$a=18-36y-by$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{36y+a-18}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\left(a=18\text{ and }y=0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9x by 2x-4xy.

$$ax^{2}+bx^{2}y=18x^{2}-36yx^{2}$$

Subtract ax^{2} from both sides.

$$bx^{2}y=18x^{2}-36yx^{2}-ax^{2}$$

Reorder the terms.

$$byx^{2}=-ax^{2}+18x^{2}-36yx^{2}$$

The equation is in standard form.

$$yx^{2}b=18x^{2}-ax^{2}-36yx^{2}$$

Divide both sides by x^{2}y.

$$\frac{yx^{2}b}{yx^{2}}=\frac{\left(18-a-36y\right)x^{2}}{yx^{2}}$$

Dividing by x^{2}y undoes the multiplication by x^{2}y.

$$b=\frac{\left(18-a-36y\right)x^{2}}{yx^{2}}$$

Divide \left(18-a-36y\right)x^{2} by x^{2}y.

$$b=\frac{18-a-36y}{y}$$