(2b+1)(2b+1)=25

Solution for (2b+1)(2b+1)=25 equation:

Simplifying
(2b + 1)(2b + 1) = 25

Reorder the terms:
(1 + 2b)(2b + 1) = 25

Reorder the terms:
(1 + 2b)(1 + 2b) = 25

Multiply (1 + 2b) * (1 + 2b)
(1(1 + 2b) + 2b * (1 + 2b)) = 25
((1 * 1 + 2b * 1) + 2b * (1 + 2b)) = 25
((1 + 2b) + 2b * (1 + 2b)) = 25
(1 + 2b + (1 * 2b + 2b * 2b)) = 25
(1 + 2b + (2b + 4b2)) = 25

Combine like terms: 2b + 2b = 4b
(1 + 4b + 4b2) = 25

Solving
1 + 4b + 4b2 = 25

Solving for variable 'b'.

Reorder the terms:
1 + -25 + 4b + 4b2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 4b + 4b2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 4b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + b + b2) = 0

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

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

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1b = 0 + 3

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

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

Divide each side by '-1'.
b = -3

Simplifying
b = -3
Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

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

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

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

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-3, 2}