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 = -0.270833333353
0.006944444447 + -0.1666666667a + a2 = -0.270833333353

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = -0.270833333353

Can't calculate square root of the right side.

The solution to this equation could not be determined.