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4\left(x-15\right)=3\left(x+60\right)
Multiply both sides of the equation by 180, the least common multiple of 45,60.
4x-60=3\left(x+60\right)
Use the distributive property to multiply 4 by x-15.
4x-60=3x+180
Use the distributive property to multiply 3 by x+60.
4x-60-3x=180
Subtract 3x from both sides.
x-60=180
Combine 4x and -3x to get x.
x=180+60
Add 60 to both sides.
x=240
Add 180 and 60 to get 240.