-4x^4+60x^3=200x^2

Solution for -4x^4+60x^3=200x^2 equation:

Simplifying
-4x4 + 60x3 = 200x2

Reorder the terms:
60x3 + -4x4 = 200x2

Solving
60x3 + -4x4 = 200x2

Solving for variable 'x'.

Reorder the terms:
-200x2 + 60x3 + -4x4 = 200x2 + -200x2

Combine like terms: 200x2 + -200x2 = 0
-200x2 + 60x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-50 + 15x + -1x2) = 0

Factor a trinomial.
4x2((-10 + x)(5 + -1x)) = 0

Ignore the factor 4.
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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 10, 5}