-5x^4+20x^3+60x^2=0

Solution for -5x^4+20x^3+60x^2=0 equation:

Simplifying
-5x4 + 20x3 + 60x2 = 0

Reorder the terms:
60x2 + 20x3 + -5x4 = 0

Solving
60x2 + 20x3 + -5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(12 + 4x + -1x2) = 0

Factor a trinomial.
5x2((6 + -1x)(2 + x)) = 0

Ignore the factor 5.
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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, 6, -2}