(4b+2)(5b+6)=0

Solution for (4b+2)(5b+6)=0 equation:

Simplifying
(4b + 2)(5b + 6) = 0

Reorder the terms:
(2 + 4b)(5b + 6) = 0

Reorder the terms:
(2 + 4b)(6 + 5b) = 0

Multiply (2 + 4b) * (6 + 5b)
(2(6 + 5b) + 4b * (6 + 5b)) = 0
((6 * 2 + 5b * 2) + 4b * (6 + 5b)) = 0
((12 + 10b) + 4b * (6 + 5b)) = 0
(12 + 10b + (6 * 4b + 5b * 4b)) = 0
(12 + 10b + (24b + 20b2)) = 0

Combine like terms: 10b + 24b = 34b
(12 + 34b + 20b2) = 0

Solving
12 + 34b + 20b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 17b + 10b2) = 0

Factor a trinomial.
2((6 + 5b)(1 + 2b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5b)' equal to zero and attempt to solve:

Simplifying
6 + 5b = 0

Solving
6 + 5b = 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 + 5b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5b = 0 + -6
5b = 0 + -6

Combine like terms: 0 + -6 = -6
5b = -6

Divide each side by '5'.
b = -1.2

Simplifying
b = -1.2
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 = {-1.2, -0.5}