(b-7)(b-10)=0

Solution for (b-7)(b-10)=0 equation:

Simplifying
(b + -7)(b + -10) = 0

Reorder the terms:
(-7 + b)(b + -10) = 0

Reorder the terms:
(-7 + b)(-10 + b) = 0

Multiply (-7 + b) * (-10 + b)
(-7(-10 + b) + b(-10 + b)) = 0
((-10 * -7 + b * -7) + b(-10 + b)) = 0
((70 + -7b) + b(-10 + b)) = 0
(70 + -7b + (-10 * b + b * b)) = 0
(70 + -7b + (-10b + b2)) = 0

Combine like terms: -7b + -10b = -17b
(70 + -17b + b2) = 0

Solving
70 + -17b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(7 + -1b)(10 + -1b) = 0

Subproblem 1
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Subproblem 2
Set the factor '(10 + -1b)' equal to zero and attempt to solve:

Simplifying
10 + -1b = 0

Solving
10 + -1b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1b = 0 + -10
-1b = 0 + -10

Combine like terms: 0 + -10 = -10
-1b = -10

Divide each side by '-1'.
b = 10

Simplifying
b = 10
Solution
b = {7, 10}