i(d)=d^2-6d

Solution for i(d)=d^2-6d equation:

Simplifying
i(d) = d2 + -6d

Multiply i * d
di = d2 + -6d

Reorder the terms:
di = -6d + d2

Solving
di = -6d + d2

Solving for variable 'd'.

Reorder the terms:
6d + di + -1d2 = -6d + d2 + 6d + -1d2

Reorder the terms:
6d + di + -1d2 = -6d + 6d + d2 + -1d2

Combine like terms: -6d + 6d = 0
6d + di + -1d2 = 0 + d2 + -1d2
6d + di + -1d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
6d + di + -1d2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(6 + i + -1d) = 0

Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0
Subproblem 2
Set the factor '(6 + i + -1d)' equal to zero and attempt to solve:

Simplifying
6 + i + -1d = 0

Reorder the terms:
6 + -1d + i = 0

Solving
6 + -1d + i = 0

Move all terms containing d to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -1d + -6 + i = 0 + -6

Reorder the terms:
6 + -6 + -1d + i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1d + i = 0 + -6
-1d + i = 0 + -6

Combine like terms: 0 + -6 = -6
-1d + i = -6

Add '-1i' to each side of the equation.
-1d + i + -1i = -6 + -1i

Combine like terms: i + -1i = 0
-1d + 0 = -6 + -1i
-1d = -6 + -1i

Divide each side by '-1'.
d = 6 + i

Simplifying
d = 6 + i
Solution
d = {0, 6 + i}