Solving the Equation (5n  12)^3 = 27
This article will guide you through the steps to solve the equation (5n  12)^3 = 27.
Understanding the Equation
The equation involves a cube, meaning a number multiplied by itself three times. We need to isolate the variable 'n' to find its value.
Steps to Solve:

Find the cube root of both sides: Since the left side of the equation is cubed, we need to take the cube root of both sides to get rid of the exponent:
โ[(5n  12)^3] = โ27
This simplifies to:
5n  12 = 3

Solve for 'n':
 Add 12 to both sides of the equation:
5n = 15
 Divide both sides by 5:
n = 3
 Add 12 to both sides of the equation:
Solution
Therefore, the solution to the equation (5n  12)^3 = 27 is n = 3.
Verification
To verify our solution, we can substitute n = 3 back into the original equation:
(5 * 3  12)^3 = (15  12)^3 = 3^3 = 27
This confirms that our solution is correct.