(b-9)(b-9)=225

Solution for (b-9)(b-9)=225 equation:

Simplifying
(b + -9)(b + -9) = 225

Reorder the terms:
(-9 + b)(b + -9) = 225

Reorder the terms:
(-9 + b)(-9 + b) = 225

Multiply (-9 + b) * (-9 + b)
(-9(-9 + b) + b(-9 + b)) = 225
((-9 * -9 + b * -9) + b(-9 + b)) = 225
((81 + -9b) + b(-9 + b)) = 225
(81 + -9b + (-9 * b + b * b)) = 225
(81 + -9b + (-9b + b2)) = 225

Combine like terms: -9b + -9b = -18b
(81 + -18b + b2) = 225

Solving
81 + -18b + b2 = 225

Solving for variable 'b'.

Reorder the terms:
81 + -225 + -18b + b2 = 225 + -225

Combine like terms: 81 + -225 = -144
-144 + -18b + b2 = 225 + -225

Combine like terms: 225 + -225 = 0
-144 + -18b + b2 = 0

Factor a trinomial.
(-6 + -1b)(24 + -1b) = 0

Subproblem 1
Set the factor '(-6 + -1b)' equal to zero and attempt to solve:

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(24 + -1b)' equal to zero and attempt to solve:

Simplifying
24 + -1b = 0

Solving
24 + -1b = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1b = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1b = 0 + -24
-1b = 0 + -24

Combine like terms: 0 + -24 = -24
-1b = -24

Divide each side by '-1'.
b = 24

Simplifying
b = 24
Solution
b = {-6, 24}