(a - d)3 + a3 + (a + d)3 = 3375

To solve the equation (a - d)3 + a3 + (a + d)3 = 3375, we can follow these steps:

Step 1: Expand the cubes (a - d)(a - d)(a - d) + a(a)(a) + (a + d)(a + d)(a + d) = 3375

Step 2: Simplify the equation (a - d)(a - d)(a - d) + a^3 + (a + d)(a + d)(a + d) = 3375

Step 3: Expand the expressions (a^3 - 3a^2d + 3ad^2 - d^3) + a^3 + (a^3 + 3a^2d + 3ad^2 + d^3) = 3375

Step 4: Combine like terms 2a^3 + 6ad^2 = 3375

Step 5: Divide both sides by 2 a^3 + 3ad^2 = 1687.5

Step 6: Subtract 3ad^2 from both sides a^3 = 1687.5 - 3ad^2

Step 7: Take the cube root of both sides a = ∛(1687.5 - 3ad^2)

So, the solution to the equation (a - d)3 + a3 + (a + d)3 = 3375 is a = ∛(1687.5 - 3ad^2).