$$3\left(6x+2\right)+15=5\left(4x+1\right)-30$$
Use the distributive property to multiply $3$ by $6x+2$.$$18x+6+15=5\left(4x+1\right)-30$$
Add $6$ and $15$ to get $21$.$$18x+21=5\left(4x+1\right)-30$$
Use the distributive property to multiply $5$ by $4x+1$.$$18x+21=20x+5-30$$
Subtract $30$ from $5$ to get $-25$.$$18x+21=20x-25$$
Subtract $20x$ from both sides.$$18x+21-20x=-25$$
Combine $18x$ and $-20x$ to get $-2x$.$$-2x+21=-25$$
Subtract $21$ from both sides.$$-2x=-25-21$$
Subtract $21$ from $-25$ to get $-46$.$$-2x=-46$$
Divide both sides by $-2$.$$x=\frac{-46}{-2}$$
Divide $-46$ by $-2$ to get $23$.$$x=23$$