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

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

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

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

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

Multiply (-3 + b) * (3 + 4b)
(-3(3 + 4b) + b(3 + 4b)) = 0
((3 * -3 + 4b * -3) + b(3 + 4b)) = 0
((-9 + -12b) + b(3 + 4b)) = 0
(-9 + -12b + (3 * b + 4b * b)) = 0
(-9 + -12b + (3b + 4b2)) = 0

Combine like terms: -12b + 3b = -9b
(-9 + -9b + 4b2) = 0

Solving
-9 + -9b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -4b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-3 + -4b)' equal to zero and attempt to solve:

Simplifying
-3 + -4b = 0

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

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

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

Divide each side by '-4'.
b = -0.75

Simplifying
b = -0.75
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-0.75, 3}