Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $12x$, the least common multiple of $4x,6x$.
$$3=2\times 5+12x\left(-7\right)$$
Multiply $2$ and $5$ to get $10$.
$$3=10+12x\left(-7\right)$$
Multiply $12$ and $-7$ to get $-84$.
$$3=10-84x$$
Swap sides so that all variable terms are on the left hand side.
$$10-84x=3$$
Subtract $10$ from both sides.
$$-84x=3-10$$
Subtract $10$ from $3$ to get $-7$.
$$-84x=-7$$
Divide both sides by $-84$.
$$x=\frac{-7}{-84}$$
Reduce the fraction $\frac{-7}{-84}$ to lowest terms by extracting and canceling out $-7$.
