$$5\left(x-3\right)-4\left(2x-1\right)=100$$
Use the distributive property to multiply $5$ by $x-3$.$$5x-15-4\left(2x-1\right)=100$$
Use the distributive property to multiply $-4$ by $2x-1$.$$5x-15-8x+4=100$$
Combine $5x$ and $-8x$ to get $-3x$.$$-3x-15+4=100$$
Add $-15$ and $4$ to get $-11$.$$-3x-11=100$$
Add $11$ to both sides.$$-3x=100+11$$
Add $100$ and $11$ to get $111$.$$-3x=111$$
Divide both sides by $-3$.$$x=\frac{111}{-3}$$
Divide $111$ by $-3$ to get $-37$.$$x=-37$$