3a-1=-3.6a(a-1)

Solution for 3a-1=-3.6a(a-1) equation:

Simplifying
3a + -1 = -3.6a(a + -1)

Reorder the terms:
-1 + 3a = -3.6a(a + -1)

Reorder the terms:
-1 + 3a = -3.6a(-1 + a)
-1 + 3a = (-1 * -3.6a + a * -3.6a)
-1 + 3a = (3.6a + -3.6a2)

Solving
-1 + 3a = 3.6a + -3.6a2

Solving for variable 'a'.

Combine like terms: 3a + -3.6a = -0.6a
-1 + -0.6a + 3.6a2 = 3.6a + -3.6a2 + -3.6a + 3.6a2

Reorder the terms:
-1 + -0.6a + 3.6a2 = 3.6a + -3.6a + -3.6a2 + 3.6a2

Combine like terms: 3.6a + -3.6a = 0.0
-1 + -0.6a + 3.6a2 = 0.0 + -3.6a2 + 3.6a2
-1 + -0.6a + 3.6a2 = -3.6a2 + 3.6a2

Combine like terms: -3.6a2 + 3.6a2 = 0.0
-1 + -0.6a + 3.6a2 = 0.0

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

Divide each side by '3.6'.
-0.2777777778 + -0.1666666667a + a2 = 0

Move the constant term to the right:

Add '0.2777777778' to each side of the equation.
-0.2777777778 + -0.1666666667a + 0.2777777778 + a2 = 0 + 0.2777777778

Reorder the terms:
-0.2777777778 + 0.2777777778 + -0.1666666667a + a2 = 0 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + -0.1666666667a + a2 = 0 + 0.2777777778
-0.1666666667a + a2 = 0 + 0.2777777778

Combine like terms: 0 + 0.2777777778 = 0.2777777778
-0.1666666667a + a2 = 0.2777777778

The a term is -0.1666666667a.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667a + 0.006944444447 + a2 = 0.2777777778 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a + a2 = 0.2777777778 + 0.006944444447

Combine like terms: 0.2777777778 + 0.006944444447 = 0.284722222247
0.006944444447 + -0.1666666667a + a2 = 0.284722222247

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = 0.284722222247

Calculate the square root of the right side: 0.533593686

Break this problem into two subproblems by setting 
(a + -0.08333333335) equal to 0.533593686 and -0.533593686.

Subproblem 1
a + -0.08333333335 = 0.533593686

Simplifying
a + -0.08333333335 = 0.533593686

Reorder the terms:
-0.08333333335 + a = 0.533593686

Solving
-0.08333333335 + a = 0.533593686

Solving for variable 'a'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + a = 0.533593686 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = 0.533593686 + 0.08333333335
a = 0.533593686 + 0.08333333335

Combine like terms: 0.533593686 + 0.08333333335 = 0.61692701935
a = 0.61692701935

Simplifying
a = 0.61692701935

Subproblem 2
a + -0.08333333335 = -0.533593686

Simplifying
a + -0.08333333335 = -0.533593686

Reorder the terms:
-0.08333333335 + a = -0.533593686

Solving
-0.08333333335 + a = -0.533593686

Solving for variable 'a'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + a = -0.533593686 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = -0.533593686 + 0.08333333335
a = -0.533593686 + 0.08333333335

Combine like terms: -0.533593686 + 0.08333333335 = -0.45026035265
a = -0.45026035265

Simplifying
a = -0.45026035265

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.61692701935, -0.45026035265}