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

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

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

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

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

Solving
4b + 2b2 = 1 + 3b

Solving for variable 'b'.

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

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

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

Combine like terms: 1 + -1 = 0
-1 + 1b + 2b2 = 0 + 3b + -3b
-1 + 1b + 2b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-1 + 1b + 2b2 = 0

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 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 + -1b = 0 + 1

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

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

Divide each side by '-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}