5x^4-10x^3=120x^2

Solution for 5x^4-10x^3=120x^2 equation:

Simplifying
5x4 + -10x3 = 120x2

Reorder the terms:
-10x3 + 5x4 = 120x2

Solving
-10x3 + 5x4 = 120x2

Solving for variable 'x'.

Reorder the terms:
-120x2 + -10x3 + 5x4 = 120x2 + -120x2

Combine like terms: 120x2 + -120x2 = 0
-120x2 + -10x3 + 5x4 = 0

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-24 + -2x + x2) = 0

Factor a trinomial.
5x2((-4 + -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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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, -4, 6}