(5b-4)(6b+6)=0

Solution for (5b-4)(6b+6)=0 equation:

Simplifying
(5b + -4)(6b + 6) = 0

Reorder the terms:
(-4 + 5b)(6b + 6) = 0

Reorder the terms:
(-4 + 5b)(6 + 6b) = 0

Multiply (-4 + 5b) * (6 + 6b)
(-4(6 + 6b) + 5b * (6 + 6b)) = 0
((6 * -4 + 6b * -4) + 5b * (6 + 6b)) = 0
((-24 + -24b) + 5b * (6 + 6b)) = 0
(-24 + -24b + (6 * 5b + 6b * 5b)) = 0
(-24 + -24b + (30b + 30b2)) = 0

Combine like terms: -24b + 30b = 6b
(-24 + 6b + 30b2) = 0

Solving
-24 + 6b + 30b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + b + 5b2) = 0

Factor a trinomial.
6((-1 + -1b)(4 + -5b)) = 0

Ignore the factor 6.
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 '(4 + -5b)' equal to zero and attempt to solve:

Simplifying
4 + -5b = 0

Solving
4 + -5b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b = 0 + -4
-5b = 0 + -4

Combine like terms: 0 + -4 = -4
-5b = -4

Divide each side by '-5'.
b = 0.8

Simplifying
b = 0.8
Solution
b = {-1, 0.8}