(b-1)(4b-3)=0

Solution for (b-1)(4b-3)=0 equation:

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

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

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

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

Combine like terms: -4b + -3b = -7b
(3 + -7b + 4b2) = 0

Solving
3 + -7b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -4b)(1 + -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 '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

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

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

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

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

Simplifying
b = 1
Solution
b = {0.75, 1}