12(х+1 1/3)=5(21/5х+7 4/15)

To solve the equation \( 12\left(x + 1 \frac{1}{3}\right) = 5\left(\frac{21}{5}x + 7 \frac{4}{15}\right) \), we should first convert the mixed numbers to improper fractions for easier calculation.

1. Convert the mixed numbers:
   • \( 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \)
   • \( 7 \frac{4}{15} = 7 + \frac{4}{15} = \frac{105}{15} + \frac{4}{15} = \frac{109}{15} \)

Now we can rewrite the equation using these improper fractions:

\[ 12\left(x + \frac{4}{3}\right) = 5\left(\frac{21}{5}x + \frac{109}{15}\right) \]

Now distribute on both sides.

Left side: \[ 12x + 12 \cdot \frac{4}{3} = 12x + 16 \]

Right side: \[ 5\left(\frac{21}{5}x + \frac{109}{15}\right) = 21x + 5 \cdot \frac{109}{15} = 21x + \frac{545}{15} \]

Now, the equation looks like this: \[ 12x + 16 = 21x + \frac{545}{15} \]

Next, we can eliminate the fractions by multiplying both sides of the equation by 15:

\[ 15(12x + 16) = 15\left(21x + \frac{545}{15}\right) \]

This simplifies to: \[ 180x + 240 = 315x + 545 \]

Now, get all terms involving \(x\) on one side and constant terms on the other side:

\[ 180x - 315x = 545 - 240 \]

This simplifies to: \[ -135x = 305 \]

Now, divide both sides by -135 to solve for \(x\):

\[ x = -\frac{305}{135} \]

We can simplify \(-\frac{305}{135}\). The greatest common divisor of 305 and 135 is 5, so:

\[ x = -\frac{61}{27} \]

Thus, the solution to the equation is:

\[ \boxed{-\frac{61}{27}} \]