(3b-5)(4b+1)=

Solution for (3b-5)(4b+1)= equation:

Simplifying
(3b + -5)(4b + 1) = 0

Reorder the terms:
(-5 + 3b)(4b + 1) = 0

Reorder the terms:
(-5 + 3b)(1 + 4b) = 0

Multiply (-5 + 3b) * (1 + 4b)
(-5(1 + 4b) + 3b * (1 + 4b)) = 0
((1 * -5 + 4b * -5) + 3b * (1 + 4b)) = 0
((-5 + -20b) + 3b * (1 + 4b)) = 0
(-5 + -20b + (1 * 3b + 4b * 3b)) = 0
(-5 + -20b + (3b + 12b2)) = 0

Combine like terms: -20b + 3b = -17b
(-5 + -17b + 12b2) = 0

Solving
-5 + -17b + 12b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -4b)(5 + -3b) = 0

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

Simplifying
-1 + -4b = 0

Solving
-1 + -4b = 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 + -4b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4b = 0 + 1
-4b = 0 + 1

Combine like terms: 0 + 1 = 1
-4b = 1

Divide each side by '-4'.
b = -0.25

Simplifying
b = -0.25
Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve:

Simplifying
5 + -3b = 0

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

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

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

Divide each side by '-3'.
b = 1.666666667

Simplifying
b = 1.666666667
Solution
b = {-0.25, 1.666666667}