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15x-3\left(x-2\right)=5\left(2x-5\right)-45
Multiply both sides of the equation by 15, the least common multiple of 5,3.
15x-3x+6=5\left(2x-5\right)-45
Use the distributive property to multiply -3 by x-2.
12x+6=5\left(2x-5\right)-45
Combine 15x and -3x to get 12x.
12x+6=10x-25-45
Use the distributive property to multiply 5 by 2x-5.
12x+6=10x-70
Subtract 45 from -25 to get -70.
12x+6-10x=-70
Subtract 10x from both sides.
2x+6=-70
Combine 12x and -10x to get 2x.
2x=-70-6
Subtract 6 from both sides.
2x=-76
Subtract 6 from -70 to get -76.
x=\frac{-76}{2}
Divide both sides by 2.
x=-38
Divide -76 by 2 to get -38.