0=3x^2-21x+3

Solution for 0=3x^2-21x+3 equation:

Simplifying
0 = 3x2 + -21x + 3

Reorder the terms:
0 = 3 + -21x + 3x2

Solving
0 = 3 + -21x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + 21x + -3x2 = 3 + -21x + 3x2 + -3 + 21x + -3x2

Reorder the terms:
-3 + 21x + -3x2 = 3 + -3 + -21x + 21x + 3x2 + -3x2

Combine like terms: 3 + -3 = 0
-3 + 21x + -3x2 = 0 + -21x + 21x + 3x2 + -3x2
-3 + 21x + -3x2 = -21x + 21x + 3x2 + -3x2

Combine like terms: -21x + 21x = 0
-3 + 21x + -3x2 = 0 + 3x2 + -3x2
-3 + 21x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-3 + 21x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 7x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + 7x + -1x2 = 0

Solving
-1 + 7x + -1x2 = 0

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

Divide each side by '-1'.
1 + -7x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -7x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x + x2 = 0 + -1
-7x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7x + x2 = -1

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -1 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + -7x + x2 = 11.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + -3.5 = 3.354101966

Simplifying
x + -3.5 = 3.354101966

Reorder the terms:
-3.5 + x = 3.354101966

Solving
-3.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.354101966 + 3.5
x = 3.354101966 + 3.5

Combine like terms: 3.354101966 + 3.5 = 6.854101966
x = 6.854101966

Simplifying
x = 6.854101966

Subproblem 2
x + -3.5 = -3.354101966

Simplifying
x + -3.5 = -3.354101966

Reorder the terms:
-3.5 + x = -3.354101966

Solving
-3.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.354101966 + 3.5
x = -3.354101966 + 3.5

Combine like terms: -3.354101966 + 3.5 = 0.145898034
x = 0.145898034

Simplifying
x = 0.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.854101966, 0.145898034}
Solution
x = {6.854101966, 0.145898034}