Solve 2ab*3a^4=6a^4b

$$2 a b \cdot 3 a ^ { 4 } = 6 a ^ { 4 } b$$

Solve for b

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=1\text{ or }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$2a^{5}b\times 3=6a^{4}b$$

Multiply 2 and 3 to get 6.

$$6a^{5}b=6a^{4}b$$

Subtract 6a^{4}b from both sides.

$$6a^{5}b-6a^{4}b=0$$

Combine all terms containing b.

$$\left(6a^{5}-6a^{4}\right)b=0$$

Divide 0 by 6a^{5}-6a^{4}.

$$b=0$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{; }a=1\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$$