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

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

Simplifying
(2b + 1)(3b + -1 + 4) = 0

Reorder the terms:
(1 + 2b)(3b + -1 + 4) = 0

Reorder the terms:
(1 + 2b)(-1 + 4 + 3b) = 0

Combine like terms: -1 + 4 = 3
(1 + 2b)(3 + 3b) = 0

Multiply (1 + 2b) * (3 + 3b)
(1(3 + 3b) + 2b * (3 + 3b)) = 0
((3 * 1 + 3b * 1) + 2b * (3 + 3b)) = 0
((3 + 3b) + 2b * (3 + 3b)) = 0
(3 + 3b + (3 * 2b + 3b * 2b)) = 0
(3 + 3b + (6b + 6b2)) = 0

Combine like terms: 3b + 6b = 9b
(3 + 9b + 6b2) = 0

Solving
3 + 9b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3b + 2b2) = 0

Factor a trinomial.
3((1 + b)(1 + 2b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

Solving
1 + b = 0

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 + -1

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2b = 0 + -1

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

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

Divide each side by '2'.
b = -0.5

Simplifying
b = -0.5
Solution
b = {-1, -0.5}