Solve A=2a*b-b*a+3b^2

$$A = 2 a \cdot b - b \cdot a + 3 b ^ { 2 }$$

Solve for a

$$\left\{\begin{matrix}a=-3b+\frac{A}{b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&A=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2ab and -ba to get ab.

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

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

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

Subtract 3b^{2} from both sides.

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

The equation is in standard form.

$$ba=A-3b^{2}$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{A-3b^{2}}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{A-3b^{2}}{b}$$

Divide -3b^{2}+A by b.

$$a=-3b+\frac{A}{b}$$

Solve for A

$$A=b\left(a+3b\right)$$

Solution Steps

Combine 2ab and -ba to get ab.

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