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50-50\times 3x+25x=25\times 2x-75
Multiply both sides of the equation by 100, the least common multiple of 2,100,4.
50-150x+25x=25\times 2x-75
Multiply -50 and 3 to get -150.
50-125x=25\times 2x-75
Combine -150x and 25x to get -125x.
50-125x=50x-75
Multiply 25 and 2 to get 50.
50-125x-50x=-75
Subtract 50x from both sides.
50-175x=-75
Combine -125x and -50x to get -175x.
-175x=-75-50
Subtract 50 from both sides.
-175x=-125
Subtract 50 from -75 to get -125.
x=\frac{-125}{-175}
Divide both sides by -175.
x=\frac{5}{7}
Reduce the fraction \frac{-125}{-175} to lowest terms by extracting and canceling out -25.