2x(3x-1)(x-9)=0

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Solution for 2x(3x-1)(x-9)=0 equation: 


Simplifying
2x(3x + -1)(x + -9) = 0

Reorder the terms:
2x(-1 + 3x)(x + -9) = 0

Reorder the terms:
2x(-1 + 3x)(-9 + x) = 0

Multiply (-1 + 3x) * (-9 + x)
2x(-1(-9 + x) + 3x * (-9 + x)) = 0
2x((-9 * -1 + x * -1) + 3x * (-9 + x)) = 0
2x((9 + -1x) + 3x * (-9 + x)) = 0
2x(9 + -1x + (-9 * 3x + x * 3x)) = 0
2x(9 + -1x + (-27x + 3x2)) = 0

Combine like terms: -1x + -27x = -28x
2x(9 + -28x + 3x2) = 0
(9 * 2x + -28x * 2x + 3x2 * 2x) = 0
(18x + -56x2 + 6x3) = 0

Solving
18x + -56x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -28x + 3x2) = 0

Factor a trinomial.
2x((1 + -3x)(9 + -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 '(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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 0.3333333333, 9}

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