0=x^4+11x^3+30x^2

Solution for 0=x^4+11x^3+30x^2 equation:

Simplifying
0 = x4 + 11x3 + 30x2

Reorder the terms:
0 = 30x2 + 11x3 + x4

Solving
0 = 30x2 + 11x3 + x4

Solving for variable 'x'.
Remove the zero:
-30x2 + -11x3 + -1x4 = 30x2 + 11x3 + x4 + -30x2 + -11x3 + -1x4

Reorder the terms:
-30x2 + -11x3 + -1x4 = 30x2 + -30x2 + 11x3 + -11x3 + x4 + -1x4

Combine like terms: 30x2 + -30x2 = 0
-30x2 + -11x3 + -1x4 = 0 + 11x3 + -11x3 + x4 + -1x4
-30x2 + -11x3 + -1x4 = 11x3 + -11x3 + x4 + -1x4

Combine like terms: 11x3 + -11x3 = 0
-30x2 + -11x3 + -1x4 = 0 + x4 + -1x4
-30x2 + -11x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-30x2 + -11x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(30 + 11x + x2) = 0

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

Ignore the factor -1.
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 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

Combine like terms: 0 + -6 = -6
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}