(b-6)x(b+3)=

Solution for (b-6)x(b+3)= equation:

Simplifying
(b + -6) * x(b + 3) = 0

Reorder the terms:
(-6 + b) * x(b + 3) = 0

Reorder the terms:
(-6 + b) * x(3 + b) = 0

Reorder the terms for easier multiplication:
x(-6 + b)(3 + b) = 0

Multiply (-6 + b) * (3 + b)
x(-6(3 + b) + b(3 + b)) = 0
x((3 * -6 + b * -6) + b(3 + b)) = 0
x((-18 + -6b) + b(3 + b)) = 0
x(-18 + -6b + (3 * b + b * b)) = 0
x(-18 + -6b + (3b + b2)) = 0

Combine like terms: -6b + 3b = -3b
x(-18 + -3b + b2) = 0
(-18 * x + -3b * x + b2 * x) = 0

Reorder the terms:
(-3bx + b2x + -18x) = 0
(-3bx + b2x + -18x) = 0

Solving
-3bx + b2x + -18x = 0

Solving for variable 'b'.

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

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing b to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(b + -6)' equal to zero and attempt to solve:

Simplifying
b + -6 = 0

Reorder the terms:
-6 + b = 0

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

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

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

Simplifying
b = 6
Subproblem 3
Set the factor '(b + 3)' equal to zero and attempt to solve:

Simplifying
b + 3 = 0

Reorder the terms:
3 + b = 0

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

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

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

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