(3b-4)(4b+6)=0

Solution for (3b-4)(4b+6)=0 equation:

Simplifying
(3b + -4)(4b + 6) = 0

Reorder the terms:
(-4 + 3b)(4b + 6) = 0

Reorder the terms:
(-4 + 3b)(6 + 4b) = 0

Multiply (-4 + 3b) * (6 + 4b)
(-4(6 + 4b) + 3b * (6 + 4b)) = 0
((6 * -4 + 4b * -4) + 3b * (6 + 4b)) = 0
((-24 + -16b) + 3b * (6 + 4b)) = 0
(-24 + -16b + (6 * 3b + 4b * 3b)) = 0
(-24 + -16b + (18b + 12b2)) = 0

Combine like terms: -16b + 18b = 2b
(-24 + 2b + 12b2) = 0

Solving
-24 + 2b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + b + 6b2) = 0

Factor a trinomial.
2((-3 + -2b)(4 + -3b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2b)' equal to zero and attempt to solve:

Simplifying
-3 + -2b = 0

Solving
-3 + -2b = 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 + -2b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2b = 0 + 3
-2b = 0 + 3

Combine like terms: 0 + 3 = 3
-2b = 3

Divide each side by '-2'.
b = -1.5

Simplifying
b = -1.5
Subproblem 2
Set the factor '(4 + -3b)' equal to zero and attempt to solve:

Simplifying
4 + -3b = 0

Solving
4 + -3b = 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 + -3b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3b = 0 + -4
-3b = 0 + -4

Combine like terms: 0 + -4 = -4
-3b = -4

Divide each side by '-3'.
b = 1.333333333

Simplifying
b = 1.333333333
Solution
b = {-1.5, 1.333333333}