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

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

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

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

Solving
0 = 18 + -9x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -18 = -18
-18 + 9x + -3x2 = 18 + -9x + 3x2 + -18 + 9x + -3x2

Reorder the terms:
-18 + 9x + -3x2 = 18 + -18 + -9x + 9x + 3x2 + -3x2

Combine like terms: 18 + -18 = 0
-18 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2
-18 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
-18 + 9x + -3x2 = 0 + 3x2 + -3x2
-18 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-18 + 9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 3x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + 3x + -1x2 = 0

Solving
-6 + 3x + -1x2 = 0

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

Divide each side by '-1'.
6 + -3x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -3x + x2 = 0 + -6

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

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3x + x2 = -3.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.