To solve the equation, we can start by simplifying the expression on the left side:

32/15 : (1/3 – 5x) = -12/5

To simplify the expression inside the parentheses, we need to find a common denominator for 1/3 and 5x. The common denominator is 3, so we can rewrite the expression as:

32/15 : (1/3 – 5x/1) = -12/5

Now, we can subtract the fractions inside the parentheses:

32/15 : (1/3 – 5x/1) = -12/5

1/3 – 5x/1 = -12/5

To combine the fractions on the left side, we need to find a common denominator. The common denominator is 3, so we can rewrite the expression as:

1/3 – 5x/1 = -12/5

Now, we can subtract the fractions:

1/3 – 5x/1 = -12/5

To subtract the fractions, we need to find a common denominator. The common denominator is 3, so we can rewrite the expression as:

1/3 – 15x/3 = -12/5

Now, we can subtract the fractions:

1/3 – 15x/3 = -12/5

To combine the fractions on the left side, we need to find a common denominator. The common denominator is 3, so we can rewrite the expression as:

(1 – 15x)/3 = -12/5

Now, we can cross-multiply to eliminate the fractions:

5(1 – 15x) = -12(3)

5 – 75x = -36

Next, we can simplify the equation:

5 – 75x = -36

To isolate the variable, we can subtract 5 from both sides:

-75x = -41

Finally, we can solve for x by dividing both sides by -75:

x = -41/-75

x = 41/75

Therefore, the solution to the equation is x = 41/75.