(X-9)(X-1)=-16

Solution for (X-9)(X-1)=-16 equation:

Simplifying
(X + -9)(X + -1) = -16

Reorder the terms:
(-9 + X)(X + -1) = -16

Reorder the terms:
(-9 + X)(-1 + X) = -16

Multiply (-9 + X) * (-1 + X)
(-9(-1 + X) + X(-1 + X)) = -16
((-1 * -9 + X * -9) + X(-1 + X)) = -16
((9 + -9X) + X(-1 + X)) = -16
(9 + -9X + (-1 * X + X * X)) = -16
(9 + -9X + (-1X + X2)) = -16

Combine like terms: -9X + -1X = -10X
(9 + -10X + X2) = -16

Solving
9 + -10X + X2 = -16

Solving for variable 'X'.

Reorder the terms:
9 + 16 + -10X + X2 = -16 + 16

Combine like terms: 9 + 16 = 25
25 + -10X + X2 = -16 + 16

Combine like terms: -16 + 16 = 0
25 + -10X + X2 = 0

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

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

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5
Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve:

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5
Solution
X = {5, 5}