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

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


Simplifying
x2(x + -3)(x + -9) = 0

Reorder the terms:
x2(-3 + x)(x + -9) = 0

Reorder the terms:
x2(-3 + x)(-9 + x) = 0

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

Combine like terms: -3x + -9x = -12x
x2(27 + -12x + x2) = 0
(27 * x2 + -12x * x2 + x2 * x2) = 0
(27x2 + -12x3 + x4) = 0

Solving
27x2 + -12x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(27 + -12x + x2) = 0

Factor a trinomial.
x2((3 + -1x)(9 + -1x)) = 0


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 '(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 '(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, 3, 9}

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