10x^6-45x^5+45x^4=

Solution for 10x^6-45x^5+45x^4= equation:

Simplifying
10x6 + -45x5 + 45x4 = 0

Reorder the terms:
45x4 + -45x5 + 10x6 = 0

Solving
45x4 + -45x5 + 10x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x4'.
5x4(9 + -9x + 2x2) = 0

Factor a trinomial.
5x4((3 + -2x)(3 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.5, 3}