Solve 0=-3b^2+(a-8)b+b

$$0 = - 3 b ^ { 2 } + ( a - 8 ) b + b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=3b+7\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-8 by b.

$$0=-3b^{2}+ab-8b+b$$

Combine -8b and b to get -7b.

$$0=-3b^{2}+ab-7b$$

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

$$-3b^{2}+ab-7b=0$$

Add 3b^{2} to both sides. Anything plus zero gives itself.

$$ab-7b=3b^{2}$$

Add 7b to both sides.

$$ab=3b^{2}+7b$$

The equation is in standard form.

$$ba=3b^{2}+7b$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{b\left(3b+7\right)}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{b\left(3b+7\right)}{b}$$

Divide b\left(7+3b\right) by b.

$$a=3b+7$$

Solve for a

$$\left\{\begin{matrix}\\a=3b+7\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-8 by b.

$$0=-3b^{2}+ab-8b+b$$

Combine -8b and b to get -7b.

$$0=-3b^{2}+ab-7b$$

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

$$-3b^{2}+ab-7b=0$$

Add 3b^{2} to both sides. Anything plus zero gives itself.

$$ab-7b=3b^{2}$$

Add 7b to both sides.

$$ab=3b^{2}+7b$$

The equation is in standard form.

$$ba=3b^{2}+7b$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{b\left(3b+7\right)}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{b\left(3b+7\right)}{b}$$

Divide b\left(7+3b\right) by b.

$$a=3b+7$$

Solve for b

$$b=\frac{a-7}{3}$$

$$b=0$$