(5b-3)(6b+5)=0

Solution for (5b-3)(6b+5)=0 equation:

Simplifying
(5b + -3)(6b + 5) = 0

Reorder the terms:
(-3 + 5b)(6b + 5) = 0

Reorder the terms:
(-3 + 5b)(5 + 6b) = 0

Multiply (-3 + 5b) * (5 + 6b)
(-3(5 + 6b) + 5b * (5 + 6b)) = 0
((5 * -3 + 6b * -3) + 5b * (5 + 6b)) = 0
((-15 + -18b) + 5b * (5 + 6b)) = 0
(-15 + -18b + (5 * 5b + 6b * 5b)) = 0
(-15 + -18b + (25b + 30b2)) = 0

Combine like terms: -18b + 25b = 7b
(-15 + 7b + 30b2) = 0

Solving
-15 + 7b + 30b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -6b)(3 + -5b) = 0

Subproblem 1
Set the factor '(-5 + -6b)' equal to zero and attempt to solve:

Simplifying
-5 + -6b = 0

Solving
-5 + -6b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6b = 0 + 5
-6b = 0 + 5

Combine like terms: 0 + 5 = 5
-6b = 5

Divide each side by '-6'.
b = -0.8333333333

Simplifying
b = -0.8333333333
Subproblem 2
Set the factor '(3 + -5b)' equal to zero and attempt to solve:

Simplifying
3 + -5b = 0

Solving
3 + -5b = 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 + -5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5b = 0 + -3
-5b = 0 + -3

Combine like terms: 0 + -3 = -3
-5b = -3

Divide each side by '-5'.
b = 0.6

Simplifying
b = 0.6
Solution
b = {-0.8333333333, 0.6}