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

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

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

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

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

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

Combine like terms: 10b + 20b = 30b
(10 + 30b + 20b2) = 0

Solving
10 + 30b + 20b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + 3b + 2b2) = 0

Factor a trinomial.
10((1 + b)(1 + 2b)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

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

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

Combine like terms: 0 + -1 = -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}