3x(x^2+6x-9)=0

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Solution for 3x(x^2+6x-9)=0 equation: 


Simplifying
3x(x2 + 6x + -9) = 0

Reorder the terms:
3x(-9 + 6x + x2) = 0
(-9 * 3x + 6x * 3x + x2 * 3x) = 0
(-27x + 18x2 + 3x3) = 0

Solving
-27x + 18x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + 6x + x2) = 0

Ignore the factor 3.

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 '(-9 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 6x + x2 = 0

Solving
-9 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 6x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 6x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 6x + x2 = 0 + 9
6x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
6x + x2 = 9

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 9 + 9

Reorder the terms:
9 + 6x + x2 = 9 + 9

Combine like terms: 9 + 9 = 18
9 + 6x + x2 = 18

Factor a perfect square on the left side:
(x + 3)(x + 3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 3) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 3 = 4.242640687

Simplifying
x + 3 = 4.242640687

Reorder the terms:
3 + x = 4.242640687

Solving
3 + x = 4.242640687

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 4.242640687 + -3

Combine like terms: 3 + -3 = 0
0 + x = 4.242640687 + -3
x = 4.242640687 + -3

Combine like terms: 4.242640687 + -3 = 1.242640687
x = 1.242640687

Simplifying
x = 1.242640687


Subproblem 2
x + 3 = -4.242640687

Simplifying
x + 3 = -4.242640687

Reorder the terms:
3 + x = -4.242640687

Solving
3 + x = -4.242640687

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -4.242640687 + -3

Combine like terms: 3 + -3 = 0
0 + x = -4.242640687 + -3
x = -4.242640687 + -3

Combine like terms: -4.242640687 + -3 = -7.242640687
x = -7.242640687

Simplifying
x = -7.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.242640687, -7.242640687}
Solution
x = {0, 1.242640687, -7.242640687}

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