d^3=d^2+30d

Solution for d^3=d^2+30d equation:

Simplifying
d3 = d2 + 30d

Reorder the terms:
d3 = 30d + d2

Solving
d3 = 30d + d2

Solving for variable 'd'.

Reorder the terms:
-30d + -1d2 + d3 = 30d + d2 + -30d + -1d2

Reorder the terms:
-30d + -1d2 + d3 = 30d + -30d + d2 + -1d2

Combine like terms: 30d + -30d = 0
-30d + -1d2 + d3 = 0 + d2 + -1d2
-30d + -1d2 + d3 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
-30d + -1d2 + d3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-30 + -1d + d2) = 0

Factor a trinomial.
d((-5 + -1d)(6 + -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 '(-5 + -1d)' equal to zero and attempt to solve:

Simplifying
-5 + -1d = 0

Solving
-5 + -1d = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1d = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1d = 0 + 5
-1d = 0 + 5

Combine like terms: 0 + 5 = 5
-1d = 5

Divide each side by '-1'.
d = -5

Simplifying
d = -5
Subproblem 3
Set the factor '(6 + -1d)' equal to zero and attempt to solve:

Simplifying
6 + -1d = 0

Solving
6 + -1d = 0

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

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

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

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

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

Simplifying
d = 6
Solution
d = {0, -5, 6}