(1-a)(3a-2)=-4a

Solution for (1-a)(3a-2)=-4a equation:

Simplifying
(1 + -1a)(3a + -2) = -4a

Reorder the terms:
(1 + -1a)(-2 + 3a) = -4a

Multiply (1 + -1a) * (-2 + 3a)
(1(-2 + 3a) + -1a * (-2 + 3a)) = -4a
((-2 * 1 + 3a * 1) + -1a * (-2 + 3a)) = -4a
((-2 + 3a) + -1a * (-2 + 3a)) = -4a
(-2 + 3a + (-2 * -1a + 3a * -1a)) = -4a
(-2 + 3a + (2a + -3a2)) = -4a

Combine like terms: 3a + 2a = 5a
(-2 + 5a + -3a2) = -4a

Solving
-2 + 5a + -3a2 = -4a

Solving for variable 'a'.

Reorder the terms:
-2 + 5a + 4a + -3a2 = -4a + 4a

Combine like terms: 5a + 4a = 9a
-2 + 9a + -3a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
-2 + 9a + -3a2 = 0

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

Divide each side by '-3'.
0.6666666667 + -3a + a2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3a + -0.6666666667 + a2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3a + a2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3a + a2 = 0 + -0.6666666667
-3a + a2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3a + a2 = -0.6666666667

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -0.6666666667 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -0.6666666667 + 2.25

Combine like terms: -0.6666666667 + 2.25 = 1.5833333333
2.25 + -3a + a2 = 1.5833333333

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 1.5833333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.258305739 and -1.258305739.

Subproblem 1
a + -1.5 = 1.258305739

Simplifying
a + -1.5 = 1.258305739

Reorder the terms:
-1.5 + a = 1.258305739

Solving
-1.5 + a = 1.258305739

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = 1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 1.258305739 + 1.5
a = 1.258305739 + 1.5

Combine like terms: 1.258305739 + 1.5 = 2.758305739
a = 2.758305739

Simplifying
a = 2.758305739

Subproblem 2
a + -1.5 = -1.258305739

Simplifying
a + -1.5 = -1.258305739

Reorder the terms:
-1.5 + a = -1.258305739

Solving
-1.5 + a = -1.258305739

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = -1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -1.258305739 + 1.5
a = -1.258305739 + 1.5

Combine like terms: -1.258305739 + 1.5 = 0.241694261
a = 0.241694261

Simplifying
a = 0.241694261

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.758305739, 0.241694261}