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

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


Simplifying
6x3 + 4x2 = 10x

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

Solving
4x2 + 6x3 = 10x

Solving for variable 'x'.

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

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

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

Factor a trinomial.
2x((-5 + -3x)(1 + -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 '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, -1.666666667, 1}

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