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

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

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

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

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

Solving for variable 'x'.
Remove the zero:
-60x2 + -20x3 + 5x4 = 60x2 + 20x3 + -5x4 + -60x2 + -20x3 + 5x4

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

Combine like terms: 60x2 + -60x2 = 0
-60x2 + -20x3 + 5x4 = 0 + 20x3 + -20x3 + -5x4 + 5x4
-60x2 + -20x3 + 5x4 = 20x3 + -20x3 + -5x4 + 5x4

Combine like terms: 20x3 + -20x3 = 0
-60x2 + -20x3 + 5x4 = 0 + -5x4 + 5x4
-60x2 + -20x3 + 5x4 = -5x4 + 5x4

Combine like terms: -5x4 + 5x4 = 0
-60x2 + -20x3 + 5x4 = 0

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

Factor a trinomial.
5x2((-2 + -1x)(6 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 3
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
Solution
x = {0, -2, 6}