(3b+2)(-7b-2)=0

Solution for (3b+2)(-7b-2)=0 equation:

Simplifying
(3b + 2)(-7b + -2) = 0

Reorder the terms:
(2 + 3b)(-7b + -2) = 0

Reorder the terms:
(2 + 3b)(-2 + -7b) = 0

Multiply (2 + 3b) * (-2 + -7b)
(2(-2 + -7b) + 3b * (-2 + -7b)) = 0
((-2 * 2 + -7b * 2) + 3b * (-2 + -7b)) = 0
((-4 + -14b) + 3b * (-2 + -7b)) = 0
(-4 + -14b + (-2 * 3b + -7b * 3b)) = 0
(-4 + -14b + (-6b + -21b2)) = 0

Combine like terms: -14b + -6b = -20b
(-4 + -20b + -21b2) = 0

Solving
-4 + -20b + -21b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 20b + 21b2) = 0

Factor a trinomial.
-1((2 + 3b)(2 + 7b)) = 0

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

Simplifying
2 + 3b = 0

Solving
2 + 3b = 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 + 3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3b = 0 + -2
3b = 0 + -2

Combine like terms: 0 + -2 = -2
3b = -2

Divide each side by '3'.
b = -0.6666666667

Simplifying
b = -0.6666666667
Subproblem 2
Set the factor '(2 + 7b)' equal to zero and attempt to solve:

Simplifying
2 + 7b = 0

Solving
2 + 7b = 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 + 7b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7b = 0 + -2
7b = 0 + -2

Combine like terms: 0 + -2 = -2
7b = -2

Divide each side by '7'.
b = -0.2857142857

Simplifying
b = -0.2857142857
Solution
b = {-0.6666666667, -0.2857142857}