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

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

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

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

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

Multiply (1 + 4b) * (2 + 4b)
(1(2 + 4b) + 4b * (2 + 4b)) = 0
((2 * 1 + 4b * 1) + 4b * (2 + 4b)) = 0
((2 + 4b) + 4b * (2 + 4b)) = 0
(2 + 4b + (2 * 4b + 4b * 4b)) = 0
(2 + 4b + (8b + 16b2)) = 0

Combine like terms: 4b + 8b = 12b
(2 + 12b + 16b2) = 0

Solving
2 + 12b + 16b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 6b + 8b2) = 0

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

Ignore the factor 2.
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 '(1 + 4b)' equal to zero and attempt to solve:

Simplifying
1 + 4b = 0

Solving
1 + 4b = 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 + 4b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4b = 0 + -1
4b = 0 + -1

Combine like terms: 0 + -1 = -1
4b = -1

Divide each side by '4'.
b = -0.25

Simplifying
b = -0.25
Solution
b = {-0.5, -0.25}