(3b-2)(b+1)=4-(b+2)(b-1)

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

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

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

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

Multiply (-2 + 3b) * (1 + b)
(-2(1 + b) + 3b * (1 + b)) = 4 + -1(b + 2)(b + -1)
((1 * -2 + b * -2) + 3b * (1 + b)) = 4 + -1(b + 2)(b + -1)
((-2 + -2b) + 3b * (1 + b)) = 4 + -1(b + 2)(b + -1)
(-2 + -2b + (1 * 3b + b * 3b)) = 4 + -1(b + 2)(b + -1)
(-2 + -2b + (3b + 3b2)) = 4 + -1(b + 2)(b + -1)

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

Reorder the terms:
-2 + 1b + 3b2 = 4 + -1(2 + b)(b + -1)

Reorder the terms:
-2 + 1b + 3b2 = 4 + -1(2 + b)(-1 + b)

Multiply (2 + b) * (-1 + b)
-2 + 1b + 3b2 = 4 + -1(2(-1 + b) + b(-1 + b))
-2 + 1b + 3b2 = 4 + -1((-1 * 2 + b * 2) + b(-1 + b))
-2 + 1b + 3b2 = 4 + -1((-2 + 2b) + b(-1 + b))
-2 + 1b + 3b2 = 4 + -1(-2 + 2b + (-1 * b + b * b))
-2 + 1b + 3b2 = 4 + -1(-2 + 2b + (-1b + b2))

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

Combine like terms: 4 + 2 = 6
-2 + 1b + 3b2 = 6 + -1b + -1b2

Solving
-2 + 1b + 3b2 = 6 + -1b + -1b2

Solving for variable 'b'.

Reorder the terms:
-2 + -6 + 1b + b + 3b2 + b2 = 6 + -1b + -1b2 + -6 + b + b2

Combine like terms: -2 + -6 = -8
-8 + 1b + b + 3b2 + b2 = 6 + -1b + -1b2 + -6 + b + b2

Combine like terms: 1b + b = 2b
-8 + 2b + 3b2 + b2 = 6 + -1b + -1b2 + -6 + b + b2

Combine like terms: 3b2 + b2 = 4b2
-8 + 2b + 4b2 = 6 + -1b + -1b2 + -6 + b + b2

Reorder the terms:
-8 + 2b + 4b2 = 6 + -6 + -1b + b + -1b2 + b2

Combine like terms: 6 + -6 = 0
-8 + 2b + 4b2 = 0 + -1b + b + -1b2 + b2
-8 + 2b + 4b2 = -1b + b + -1b2 + b2

Combine like terms: -1b + b = 0
-8 + 2b + 4b2 = 0 + -1b2 + b2
-8 + 2b + 4b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
-8 + 2b + 4b2 = 0

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

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

Simplifying
-4 + b + 2b2 = 0

Solving
-4 + b + 2b2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5b + 0.25 + b2 = 2 + 0.25

Reorder the terms:
0.25 + 0.5b + b2 = 2 + 0.25

Combine like terms: 2 + 0.25 = 2.25
0.25 + 0.5b + b2 = 2.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(b + 0.5) equal to 1.5 and -1.5.

Subproblem 1
b + 0.5 = 1.5

Simplifying
b + 0.5 = 1.5

Reorder the terms:
0.5 + b = 1.5

Solving
0.5 + b = 1.5

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 1.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 1.5 + -0.5
b = 1.5 + -0.5

Combine like terms: 1.5 + -0.5 = 1
b = 1

Simplifying
b = 1

Subproblem 2
b + 0.5 = -1.5

Simplifying
b + 0.5 = -1.5

Reorder the terms:
0.5 + b = -1.5

Solving
0.5 + b = -1.5

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -1.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -1.5 + -0.5
b = -1.5 + -0.5

Combine like terms: -1.5 + -0.5 = -2
b = -2

Simplifying
b = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1, -2}
Solution
b = {1, -2}