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

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

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

Reorder the terms:
3b(1 + 2b) = 4 + -2b
(1 * 3b + 2b * 3b) = 4 + -2b
(3b + 6b2) = 4 + -2b

Solving
3b + 6b2 = 4 + -2b

Solving for variable 'b'.

Reorder the terms:
-4 + 3b + 2b + 6b2 = 4 + -2b + -4 + 2b

Combine like terms: 3b + 2b = 5b
-4 + 5b + 6b2 = 4 + -2b + -4 + 2b

Reorder the terms:
-4 + 5b + 6b2 = 4 + -4 + -2b + 2b

Combine like terms: 4 + -4 = 0
-4 + 5b + 6b2 = 0 + -2b + 2b
-4 + 5b + 6b2 = -2b + 2b

Combine like terms: -2b + 2b = 0
-4 + 5b + 6b2 = 0

Factor a trinomial.
(-4 + -3b)(1 + -2b) = 0

Subproblem 1
Set the factor '(-4 + -3b)' equal to zero and attempt to solve:

Simplifying
-4 + -3b = 0

Solving
-4 + -3b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3b = 0 + 4
-3b = 0 + 4

Combine like terms: 0 + 4 = 4
-3b = 4

Divide each side by '-3'.
b = -1.333333333

Simplifying
b = -1.333333333
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 = {-1.333333333, 0.5}