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3\times 32c+4\times 2c=7
Multiply both sides of the equation by 12, the least common multiple of 4,3,12.
96c+4\times 2c=7
Multiply 3 and 32 to get 96.
96c+8c=7
Multiply 4 and 2 to get 8.
104c=7
Combine 96c and 8c to get 104c.
c=\frac{7}{104}
Divide both sides by 104.