-3(2-a)a=1

Solution for -3(2-a)a=1 equation:

Simplifying
-3(2 + -1a) * a = 1

Reorder the terms for easier multiplication:
-3a(2 + -1a) = 1
(2 * -3a + -1a * -3a) = 1
(-6a + 3a2) = 1

Solving
-6a + 3a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + -6a + 3a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -6a + 3a2 = 0

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

Divide each side by '3'.
-0.3333333333 + -2a + a2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2a + 0.3333333333 + a2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2a + a2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2a + a2 = 0 + 0.3333333333
-2a + a2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2a + a2 = 0.3333333333

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 = 0.3333333333 + 1

Reorder the terms:
1 + -2a + a2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + -2a + a2 = 1.3333333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(a + -1) equal to 1.154700538 and -1.154700538.

Subproblem 1
a + -1 = 1.154700538

Simplifying
a + -1 = 1.154700538

Reorder the terms:
-1 + a = 1.154700538

Solving
-1 + a = 1.154700538

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 = 1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.154700538 + 1
a = 1.154700538 + 1

Combine like terms: 1.154700538 + 1 = 2.154700538
a = 2.154700538

Simplifying
a = 2.154700538

Subproblem 2
a + -1 = -1.154700538

Simplifying
a + -1 = -1.154700538

Reorder the terms:
-1 + a = -1.154700538

Solving
-1 + a = -1.154700538

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 = -1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.154700538 + 1
a = -1.154700538 + 1

Combine like terms: -1.154700538 + 1 = -0.154700538
a = -0.154700538

Simplifying
a = -0.154700538

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.154700538, -0.154700538}