x(-3x+6)(-9x-3)=0

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Solution for x(-3x+6)(-9x-3)=0 equation: 


Simplifying
x(-3x + 6)(-9x + -3) = 0

Reorder the terms:
x(6 + -3x)(-9x + -3) = 0

Reorder the terms:
x(6 + -3x)(-3 + -9x) = 0

Multiply (6 + -3x) * (-3 + -9x)
x(6(-3 + -9x) + -3x * (-3 + -9x)) = 0
x((-3 * 6 + -9x * 6) + -3x * (-3 + -9x)) = 0
x((-18 + -54x) + -3x * (-3 + -9x)) = 0
x(-18 + -54x + (-3 * -3x + -9x * -3x)) = 0
x(-18 + -54x + (9x + 27x2)) = 0

Combine like terms: -54x + 9x = -45x
x(-18 + -45x + 27x2) = 0
(-18 * x + -45x * x + 27x2 * x) = 0
(-18x + -45x2 + 27x3) = 0

Solving
-18x + -45x2 + 27x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-2 + -5x + 3x2) = 0

Factor a trinomial.
9x((-1 + -3x)(2 + -1x)) = 0

Ignore the factor 9.

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 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -0.3333333333, 2}

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