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4\times 2m+3\times 3m=204
Multiply both sides of the equation by 12, the least common multiple of 3,4.
8m+3\times 3m=204
Multiply 4 and 2 to get 8.
8m+9m=204
Multiply 3 and 3 to get 9.
17m=204
Combine 8m and 9m to get 17m.
m=\frac{204}{17}
Divide both sides by 17.
m=12
Divide 204 by 17 to get 12.