(6b-18)(2b+2)=0

Solution for (6b-18)(2b+2)=0 equation:

Simplifying
(6b + -18)(2b + 2) = 0

Reorder the terms:
(-18 + 6b)(2b + 2) = 0

Reorder the terms:
(-18 + 6b)(2 + 2b) = 0

Multiply (-18 + 6b) * (2 + 2b)
(-18(2 + 2b) + 6b * (2 + 2b)) = 0
((2 * -18 + 2b * -18) + 6b * (2 + 2b)) = 0
((-36 + -36b) + 6b * (2 + 2b)) = 0
(-36 + -36b + (2 * 6b + 2b * 6b)) = 0
(-36 + -36b + (12b + 12b2)) = 0

Combine like terms: -36b + 12b = -24b
(-36 + -24b + 12b2) = 0

Solving
-36 + -24b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + -2b + b2) = 0

Factor a trinomial.
12((-1 + -1b)(3 + -1b)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + -1b)' equal to zero and attempt to solve:

Simplifying
-1 + -1b = 0

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

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

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

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

Simplifying
b = -1
Subproblem 2
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
Solution
b = {-1, 3}