Solve a/2*b/3=3a*2b/6

$$\frac { a } { 2 } \times \frac { b } { 3 } = \frac { 3 a \times 2 b } { 6 }$$

Solve for a

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$ab=3a\times 2b$$

Multiply 3 and 2 to get 6.

$$ab=6ab$$

Subtract 6ab from both sides.

$$ab-6ab=0$$

Combine ab and -6ab to get -5ab.

$$-5ab=0$$

The equation is in standard form.

$$\left(-5b\right)a=0$$

Divide 0 by -5b.

$$a=0$$

Solve for b

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$ab=3a\times 2b$$

Multiply 3 and 2 to get 6.

$$ab=6ab$$

Subtract 6ab from both sides.

$$ab-6ab=0$$

Combine ab and -6ab to get -5ab.

$$-5ab=0$$

The equation is in standard form.

$$\left(-5a\right)b=0$$

Divide 0 by -5a.

$$b=0$$