0=3x^2-9x+6

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

Simplifying
0 = 3x2 + -9x + 6

Reorder the terms:
0 = 6 + -9x + 3x2

Solving
0 = 6 + -9x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 9x + -3x2 = 6 + -9x + 3x2 + -6 + 9x + -3x2

Reorder the terms:
-6 + 9x + -3x2 = 6 + -6 + -9x + 9x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
-6 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2
-6 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
-6 + 9x + -3x2 = 0 + 3x2 + -3x2
-6 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + 9x + -3x2 = 0

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

Factor a trinomial.
3((-2 + x)(1 + -1x)) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

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

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

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {2, 1}