(2b+1)(b-3)=6b+3

Solution for (2b+1)(b-3)=6b+3 equation:

Simplifying
(2b + 1)(b + -3) = 6b + 3

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

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

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

Combine like terms: 1b + -6b = -5b
(-3 + -5b + 2b2) = 6b + 3

Reorder the terms:
-3 + -5b + 2b2 = 3 + 6b

Solving
-3 + -5b + 2b2 = 3 + 6b

Solving for variable 'b'.

Reorder the terms:
-3 + -3 + -5b + -6b + 2b2 = 3 + 6b + -3 + -6b

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

Combine like terms: -5b + -6b = -11b
-6 + -11b + 2b2 = 3 + 6b + -3 + -6b

Reorder the terms:
-6 + -11b + 2b2 = 3 + -3 + 6b + -6b

Combine like terms: 3 + -3 = 0
-6 + -11b + 2b2 = 0 + 6b + -6b
-6 + -11b + 2b2 = 6b + -6b

Combine like terms: 6b + -6b = 0
-6 + -11b + 2b2 = 0

Factor a trinomial.
(-1 + -2b)(6 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-0.5, 6}