=(b-3)(b-5)

Solution for =(b-3)(b-5) equation:

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

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

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

Multiply (-3 + b) * (-5 + b)
0 = (-3(-5 + b) + b(-5 + b))
0 = ((-5 * -3 + b * -3) + b(-5 + b))
0 = ((15 + -3b) + b(-5 + b))
0 = (15 + -3b + (-5 * b + b * b))
0 = (15 + -3b + (-5b + b2))

Combine like terms: -3b + -5b = -8b
0 = (15 + -8b + b2)

Solving
0 = 15 + -8b + b2

Solving for variable 'b'.

Combine like terms: 0 + -15 = -15
-15 + 8b + -1b2 = 15 + -8b + b2 + -15 + 8b + -1b2

Reorder the terms:
-15 + 8b + -1b2 = 15 + -15 + -8b + 8b + b2 + -1b2

Combine like terms: 15 + -15 = 0
-15 + 8b + -1b2 = 0 + -8b + 8b + b2 + -1b2
-15 + 8b + -1b2 = -8b + 8b + b2 + -1b2

Combine like terms: -8b + 8b = 0
-15 + 8b + -1b2 = 0 + b2 + -1b2
-15 + 8b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
-15 + 8b + -1b2 = 0

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

Subproblem 1
Set the factor '(-5 + b)' equal to zero and attempt to solve:

Simplifying
-5 + b = 0

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

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

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

Simplifying
b = 5
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 = {5, 3}