(3b+7)(5b-6)=0

Solution for (3b+7)(5b-6)=0 equation:

Simplifying
(3b + 7)(5b + -6) = 0

Reorder the terms:
(7 + 3b)(5b + -6) = 0

Reorder the terms:
(7 + 3b)(-6 + 5b) = 0

Multiply (7 + 3b) * (-6 + 5b)
(7(-6 + 5b) + 3b * (-6 + 5b)) = 0
((-6 * 7 + 5b * 7) + 3b * (-6 + 5b)) = 0
((-42 + 35b) + 3b * (-6 + 5b)) = 0
(-42 + 35b + (-6 * 3b + 5b * 3b)) = 0
(-42 + 35b + (-18b + 15b2)) = 0

Combine like terms: 35b + -18b = 17b
(-42 + 17b + 15b2) = 0

Solving
-42 + 17b + 15b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-7 + -3b)(6 + -5b) = 0

Subproblem 1
Set the factor '(-7 + -3b)' equal to zero and attempt to solve:

Simplifying
-7 + -3b = 0

Solving
-7 + -3b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3b = 0 + 7
-3b = 0 + 7

Combine like terms: 0 + 7 = 7
-3b = 7

Divide each side by '-3'.
b = -2.333333333

Simplifying
b = -2.333333333
Subproblem 2
Set the factor '(6 + -5b)' equal to zero and attempt to solve:

Simplifying
6 + -5b = 0

Solving
6 + -5b = 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 + -5b = 0 + -6

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

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

Divide each side by '-5'.
b = 1.2

Simplifying
b = 1.2
Solution
b = {-2.333333333, 1.2}