3a^2-6a=3

Solution for 3a^2-6a=3 equation:

Simplifying
3a2 + -6a = 3

Reorder the terms:
-6a + 3a2 = 3

Solving
-6a + 3a2 = 3

Solving for variable 'a'.

Reorder the terms:
-3 + -6a + 3a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2a + a2)' equal to zero and attempt to solve:

Simplifying
-1 + -2a + a2 = 0

Solving
-1 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + -2a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a + a2 = 0 + 1
-2a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2a + a2 = 1

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

Add '1' to each side of the equation.
-2a + 1 + a2 = 1 + 1

Reorder the terms:
1 + -2a + a2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2a + a2 = 2

Factor a perfect square on the left side:
(a + -1)(a + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(a + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
a + -1 = 1.414213562

Simplifying
a + -1 = 1.414213562

Reorder the terms:
-1 + a = 1.414213562

Solving
-1 + a = 1.414213562

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.414213562 + 1
a = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
a = 2.414213562

Simplifying
a = 2.414213562

Subproblem 2
a + -1 = -1.414213562

Simplifying
a + -1 = -1.414213562

Reorder the terms:
-1 + a = -1.414213562

Solving
-1 + a = -1.414213562

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.414213562 + 1
a = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
a = -0.414213562

Simplifying
a = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.414213562, -0.414213562}
Solution
a = {2.414213562, -0.414213562}