a^4=a^3-30a^2

Solution for a^4=a^3-30a^2 equation:

Simplifying
a4 = a3 + -30a2

Reorder the terms:
a4 = -30a2 + a3

Solving
a4 = -30a2 + a3

Solving for variable 'a'.

Reorder the terms:
30a2 + -1a3 + a4 = -30a2 + a3 + 30a2 + -1a3

Reorder the terms:
30a2 + -1a3 + a4 = -30a2 + 30a2 + a3 + -1a3

Combine like terms: -30a2 + 30a2 = 0
30a2 + -1a3 + a4 = 0 + a3 + -1a3
30a2 + -1a3 + a4 = a3 + -1a3

Combine like terms: a3 + -1a3 = 0
30a2 + -1a3 + a4 = 0

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(30 + -1a + a2) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(30 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
30 + -1a + a2 = 0

Solving
30 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -1a + -30 + a2 = 0 + -30

Reorder the terms:
30 + -30 + -1a + a2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1a + a2 = 0 + -30
-1a + a2 = 0 + -30

Combine like terms: 0 + -30 = -30
-1a + a2 = -30

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -30 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -30 + 0.25

Combine like terms: -30 + 0.25 = -29.75
0.25 + -1a + a2 = -29.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -29.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}