2x^3-10x^2+40x=8x

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Solution for 2x^3-10x^2+40x=8x equation: 


Simplifying
2x3 + -10x2 + 40x = 8x

Reorder the terms:
40x + -10x2 + 2x3 = 8x

Solving
40x + -10x2 + 2x3 = 8x

Solving for variable 'x'.

Reorder the terms:
40x + -8x + -10x2 + 2x3 = 8x + -8x

Combine like terms: 40x + -8x = 32x
32x + -10x2 + 2x3 = 8x + -8x

Combine like terms: 8x + -8x = 0
32x + -10x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + -5x + x2) = 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 '(16 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -5x + x2 = 0

Solving
16 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -5x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -5x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5x + x2 = 0 + -16
-5x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-5x + x2 = -16

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -16 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -16 + 6.25

Combine like terms: -16 + 6.25 = -9.75
6.25 + -5x + x2 = -9.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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