4x^3-10x^2=6x

Solution for 4x^3-10x^2=6x equation:

Simplifying
4x3 + -10x2 = 6x

Reorder the terms:
-10x2 + 4x3 = 6x

Solving
-10x2 + 4x3 = 6x

Solving for variable 'x'.

Reorder the terms:
-6x + -10x2 + 4x3 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6x + -10x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + -5x + 2x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {0, -0.5, 3}