(4b+1)(5b-2)=

Solution for (4b+1)(5b-2)= equation:

Simplifying
(4b + 1)(5b + -2) = 0

Reorder the terms:
(1 + 4b)(5b + -2) = 0

Reorder the terms:
(1 + 4b)(-2 + 5b) = 0

Multiply (1 + 4b) * (-2 + 5b)
(1(-2 + 5b) + 4b * (-2 + 5b)) = 0
((-2 * 1 + 5b * 1) + 4b * (-2 + 5b)) = 0
((-2 + 5b) + 4b * (-2 + 5b)) = 0
(-2 + 5b + (-2 * 4b + 5b * 4b)) = 0
(-2 + 5b + (-8b + 20b2)) = 0

Combine like terms: 5b + -8b = -3b
(-2 + -3b + 20b2) = 0

Solving
-2 + -3b + 20b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -4b)(2 + -5b) = 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 '(2 + -5b)' equal to zero and attempt to solve:

Simplifying
2 + -5b = 0

Solving
2 + -5b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5b = 0 + -2
-5b = 0 + -2

Combine like terms: 0 + -2 = -2
-5b = -2

Divide each side by '-5'.
b = 0.4

Simplifying
b = 0.4
Solution
b = {-0.25, 0.4}