0=3x^2-15x+6

Solution for 0=3x^2-15x+6 equation:

Simplifying
0 = 3x2 + -15x + 6

Reorder the terms:
0 = 6 + -15x + 3x2

Solving
0 = 6 + -15x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 15x + -3x2 = 6 + -15x + 3x2 + -6 + 15x + -3x2

Reorder the terms:
-6 + 15x + -3x2 = 6 + -6 + -15x + 15x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
-6 + 15x + -3x2 = 0 + -15x + 15x + 3x2 + -3x2
-6 + 15x + -3x2 = -15x + 15x + 3x2 + -3x2

Combine like terms: -15x + 15x = 0
-6 + 15x + -3x2 = 0 + 3x2 + -3x2
-6 + 15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + 15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 5x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
-2 + 5x + -1x2 = 0

Solving
-2 + 5x + -1x2 = 0

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

Divide each side by '-1'.
2 + -5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x + x2 = 0 + -2
-5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5x + x2 = -2

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5x + x2 = 4.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + -2.5 = 2.061552813

Simplifying
x + -2.5 = 2.061552813

Reorder the terms:
-2.5 + x = 2.061552813

Solving
-2.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.061552813 + 2.5
x = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
x = 4.561552813

Simplifying
x = 4.561552813

Subproblem 2
x + -2.5 = -2.061552813

Simplifying
x + -2.5 = -2.061552813

Reorder the terms:
-2.5 + x = -2.061552813

Solving
-2.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.061552813 + 2.5
x = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
x = 0.438447187

Simplifying
x = 0.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.561552813, 0.438447187}
Solution
x = {4.561552813, 0.438447187}