(x^2-6x)(x-2)+3x=0

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Solution for (x^2-6x)(x-2)+3x=0 equation: 


Simplifying
(x2 + -6x)(x + -2) + 3x = 0

Reorder the terms:
(-6x + x2)(x + -2) + 3x = 0

Reorder the terms:
(-6x + x2)(-2 + x) + 3x = 0

Multiply (-6x + x2) * (-2 + x)
(-6x * (-2 + x) + x2(-2 + x)) + 3x = 0
((-2 * -6x + x * -6x) + x2(-2 + x)) + 3x = 0
((12x + -6x2) + x2(-2 + x)) + 3x = 0
(12x + -6x2 + (-2 * x2 + x * x2)) + 3x = 0
(12x + -6x2 + (-2x2 + x3)) + 3x = 0

Combine like terms: -6x2 + -2x2 = -8x2
(12x + -8x2 + x3) + 3x = 0

Reorder the terms:
12x + 3x + -8x2 + x3 = 0

Combine like terms: 12x + 3x = 15x
15x + -8x2 + x3 = 0

Solving
15x + -8x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -8x + x2) = 0

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


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 '(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

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 3, 5}

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