Solve x=5a^2+2a+b+ab-7

$$x = 5 a ^ { 2 } + 2 a + b + a b - 7$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{-x+5a^{2}+2a-7}{a+1}\text{, }&a\neq -1\\b\in \mathrm{C}\text{, }&x=-4\text{ and }a=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a^{2}+2a+b+ab-7=x$$

Subtract 5a^{2} from both sides.

$$2a+b+ab-7=x-5a^{2}$$

Subtract 2a from both sides.

$$b+ab-7=x-5a^{2}-2a$$

Add 7 to both sides.

$$b+ab=x-5a^{2}-2a+7$$

Combine all terms containing b.

$$\left(1+a\right)b=x-5a^{2}-2a+7$$

The equation is in standard form.

$$\left(a+1\right)b=x-5a^{2}-2a+7$$

Divide both sides by 1+a.

$$\frac{\left(a+1\right)b}{a+1}=\frac{x-5a^{2}-2a+7}{a+1}$$

Dividing by 1+a undoes the multiplication by 1+a.

$$b=\frac{x-5a^{2}-2a+7}{a+1}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{-x+5a^{2}+2a-7}{a+1}\text{, }&a\neq -1\\b\in \mathrm{R}\text{, }&x=-4\text{ and }a=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a^{2}+2a+b+ab-7=x$$

Subtract 5a^{2} from both sides.

$$2a+b+ab-7=x-5a^{2}$$

Subtract 2a from both sides.

$$b+ab-7=x-5a^{2}-2a$$

Add 7 to both sides.

$$b+ab=x-5a^{2}-2a+7$$

Combine all terms containing b.

$$\left(1+a\right)b=x-5a^{2}-2a+7$$

The equation is in standard form.

$$\left(a+1\right)b=x-5a^{2}-2a+7$$

Divide both sides by 1+a.

$$\frac{\left(a+1\right)b}{a+1}=\frac{x-5a^{2}-2a+7}{a+1}$$

Dividing by 1+a undoes the multiplication by 1+a.

$$b=\frac{x-5a^{2}-2a+7}{a+1}$$

Solve for a (complex solution)

$$a=\frac{\sqrt{20x+b^{2}-16b+144}}{10}-\frac{b}{10}-\frac{1}{5}$$

$$a=-\frac{\sqrt{20x+b^{2}-16b+144}}{10}-\frac{b}{10}-\frac{1}{5}$$

Solve for a

$$a=\frac{\sqrt{20x+b^{2}-16b+144}}{10}-\frac{b}{10}-\frac{1}{5}$$

$$a=-\frac{\sqrt{20x+b^{2}-16b+144}}{10}-\frac{b}{10}-\frac{1}{5}\text{, }x\geq -\frac{b^{2}}{20}+\frac{4b}{5}-\frac{36}{5}$$