Solve quad30x-40=a(6x-b)

$$\quad 30 x - 40 = a ( 6 x - b )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{10\left(3x-4\right)}{b-6x}\text{, }&x\neq \frac{b}{6}\\a\in \mathrm{C}\text{, }&x=\frac{4}{3}\text{ and }b=8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 6x-b.

$$30x-40=6ax-ab$$

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

$$6ax-ab=30x-40$$

Combine all terms containing a.

$$\left(6x-b\right)a=30x-40$$

Divide both sides by 6x-b.

$$\frac{\left(6x-b\right)a}{6x-b}=\frac{30x-40}{6x-b}$$

Dividing by 6x-b undoes the multiplication by 6x-b.

$$a=\frac{30x-40}{6x-b}$$

Divide 30x-40 by 6x-b.

$$a=\frac{10\left(3x-4\right)}{6x-b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{2\left(3ax-15x+20\right)}{a}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&x=\frac{4}{3}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 6x-b.

$$30x-40=6ax-ab$$

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

$$6ax-ab=30x-40$$

Subtract 6ax from both sides.

$$-ab=30x-40-6ax$$

The equation is in standard form.

$$\left(-a\right)b=-6ax+30x-40$$

Divide both sides by -a.

$$\frac{\left(-a\right)b}{-a}=\frac{-6ax+30x-40}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b=\frac{-6ax+30x-40}{-a}$$

Divide 30x-40-6ax by -a.

$$b=-\frac{2\left(-3ax+15x-20\right)}{a}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{10\left(3x-4\right)}{b-6x}\text{, }&x\neq \frac{b}{6}\\a\in \mathrm{R}\text{, }&x=\frac{4}{3}\text{ and }b=8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 6x-b.

$$30x-40=6ax-ab$$

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

$$6ax-ab=30x-40$$

Combine all terms containing a.

$$\left(6x-b\right)a=30x-40$$

Divide both sides by 6x-b.

$$\frac{\left(6x-b\right)a}{6x-b}=\frac{30x-40}{6x-b}$$

Dividing by 6x-b undoes the multiplication by 6x-b.

$$a=\frac{30x-40}{6x-b}$$

Divide 30x-40 by 6x-b.

$$a=\frac{10\left(3x-4\right)}{6x-b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{2\left(3ax-15x+20\right)}{a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&x=\frac{4}{3}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 6x-b.

$$30x-40=6ax-ab$$

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

$$6ax-ab=30x-40$$

Subtract 6ax from both sides.

$$-ab=30x-40-6ax$$

The equation is in standard form.

$$\left(-a\right)b=-6ax+30x-40$$

Divide both sides by -a.

$$\frac{\left(-a\right)b}{-a}=\frac{-6ax+30x-40}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b=\frac{-6ax+30x-40}{-a}$$

Divide 30x-40-6ax by -a.

$$b=-\frac{2\left(-3ax+15x-20\right)}{a}$$