0=x^4-x^3-30x^2

Solution for 0=x^4-x^3-30x^2 equation:

Simplifying
0 = x4 + -1x3 + -30x2

Reorder the terms:
0 = -30x2 + -1x3 + x4

Solving
0 = -30x2 + -1x3 + x4

Solving for variable 'x'.
Remove the zero:
30x2 + x3 + -1x4 = -30x2 + -1x3 + x4 + 30x2 + x3 + -1x4

Reorder the terms:
30x2 + x3 + -1x4 = -30x2 + 30x2 + -1x3 + x3 + x4 + -1x4

Combine like terms: -30x2 + 30x2 = 0
30x2 + x3 + -1x4 = 0 + -1x3 + x3 + x4 + -1x4
30x2 + x3 + -1x4 = -1x3 + x3 + x4 + -1x4

Combine like terms: -1x3 + x3 = 0
30x2 + x3 + -1x4 = 0 + x4 + -1x4
30x2 + x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
30x2 + x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(30 + x + -1x2) = 0

Factor a trinomial.
x2((6 + -1x)(5 + x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

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