6x(x^3-2x^2+5x)=

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Solution for 6x(x^3-2x^2+5x)= equation: 


Simplifying
6x(x3 + -2x2 + 5x) = 0

Reorder the terms:
6x(5x + -2x2 + x3) = 0
(5x * 6x + -2x2 * 6x + x3 * 6x) = 0
(30x2 + -12x3 + 6x4) = 0

Solving
30x2 + -12x3 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(5 + -2x + x2) = 0

Ignore the factor 6.

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 '(5 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x + x2 = 0

Solving
5 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x + x2 = 0 + -5
-2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x + x2 = -5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -5 + 1

Reorder the terms:
1 + -2x + x2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + -2x + x2 = -4

Factor a perfect square on the left side:
(x + -1)(x + -1) = -4

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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