(2b-6)(3b+18)=0

Solution for (2b-6)(3b+18)=0 equation:

Simplifying
(2b + -6)(3b + 18) = 0

Reorder the terms:
(-6 + 2b)(3b + 18) = 0

Reorder the terms:
(-6 + 2b)(18 + 3b) = 0

Multiply (-6 + 2b) * (18 + 3b)
(-6(18 + 3b) + 2b * (18 + 3b)) = 0
((18 * -6 + 3b * -6) + 2b * (18 + 3b)) = 0
((-108 + -18b) + 2b * (18 + 3b)) = 0
(-108 + -18b + (18 * 2b + 3b * 2b)) = 0
(-108 + -18b + (36b + 6b2)) = 0

Combine like terms: -18b + 36b = 18b
(-108 + 18b + 6b2) = 0

Solving
-108 + 18b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + 3b + b2) = 0

Factor a trinomial.
6((-6 + -1b)(3 + -1b)) = 0

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

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 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 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
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 = {-6, 3}