3-2b^2-4b=4

Solution for 3-2b^2-4b=4 equation:

Simplifying
3 + -2b2 + -4b = 4

Reorder the terms:
3 + -4b + -2b2 = 4

Solving
3 + -4b + -2b2 = 4

Solving for variable 'b'.

Reorder the terms:
3 + -4 + -4b + -2b2 = 4 + -4

Combine like terms: 3 + -4 = -1
-1 + -4b + -2b2 = 4 + -4

Combine like terms: 4 + -4 = 0
-1 + -4b + -2b2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 4b + 2b2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 4b + 2b2)' equal to zero and attempt to solve:

Simplifying
1 + 4b + 2b2 = 0

Solving
1 + 4b + 2b2 = 0

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

Divide each side by '2'.
0.5 + 2b + b2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2b + -0.5 + b2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2b + b2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2b + b2 = 0 + -0.5
2b + b2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2b + b2 = -0.5

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

Add '1' to each side of the equation.
2b + 1 + b2 = -0.5 + 1

Reorder the terms:
1 + 2b + b2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2b + b2 = 0.5

Factor a perfect square on the left side:
(b + 1)(b + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(b + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
b + 1 = 0.707106781

Simplifying
b + 1 = 0.707106781

Reorder the terms:
1 + b = 0.707106781

Solving
1 + b = 0.707106781

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + b = 0.707106781 + -1
b = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
b = -0.292893219

Simplifying
b = -0.292893219

Subproblem 2
b + 1 = -0.707106781

Simplifying
b + 1 = -0.707106781

Reorder the terms:
1 + b = -0.707106781

Solving
1 + b = -0.707106781

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + b = -0.707106781 + -1
b = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
b = -1.707106781

Simplifying
b = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.292893219, -1.707106781}
Solution
b = {-0.292893219, -1.707106781}