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

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

Simplifying
0 = 3(x2 + -2x + -9)

Reorder the terms:
0 = 3(-9 + -2x + x2)
0 = (-9 * 3 + -2x * 3 + x2 * 3)
0 = (-27 + -6x + 3x2)

Solving
0 = -27 + -6x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 27 = 27
27 + 6x + -3x2 = -27 + -6x + 3x2 + 27 + 6x + -3x2

Reorder the terms:
27 + 6x + -3x2 = -27 + 27 + -6x + 6x + 3x2 + -3x2

Combine like terms: -27 + 27 = 0
27 + 6x + -3x2 = 0 + -6x + 6x + 3x2 + -3x2
27 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
27 + 6x + -3x2 = 0 + 3x2 + -3x2
27 + 6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
27 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 2x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
9 + 2x + -1x2 = 0

Solving
9 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + -2x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x + x2 = 0 + 9
-2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2x + x2 = 9

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + -2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2x + x2 = 10

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -1 = 3.16227766

Simplifying
x + -1 = 3.16227766

Reorder the terms:
-1 + x = 3.16227766

Solving
-1 + x = 3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.16227766 + 1
x = 3.16227766 + 1

Combine like terms: 3.16227766 + 1 = 4.16227766
x = 4.16227766

Simplifying
x = 4.16227766

Subproblem 2
x + -1 = -3.16227766

Simplifying
x + -1 = -3.16227766

Reorder the terms:
-1 + x = -3.16227766

Solving
-1 + x = -3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.16227766 + 1
x = -3.16227766 + 1

Combine like terms: -3.16227766 + 1 = -2.16227766
x = -2.16227766

Simplifying
x = -2.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.16227766, -2.16227766}
Solution
x = {4.16227766, -2.16227766}