(x-9)(x-16)=0

Solution for (x-9)(x-16)=0 equation:

Simplifying
(x + -9)(x + -16) = 0

Reorder the terms:
(-9 + x)(x + -16) = 0

Reorder the terms:
(-9 + x)(-16 + x) = 0

Multiply (-9 + x) * (-16 + x)
(-9(-16 + x) + x(-16 + x)) = 0
((-16 * -9 + x * -9) + x(-16 + x)) = 0
((144 + -9x) + x(-16 + x)) = 0
(144 + -9x + (-16 * x + x * x)) = 0
(144 + -9x + (-16x + x2)) = 0

Combine like terms: -9x + -16x = -25x
(144 + -25x + x2) = 0

Solving
144 + -25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {9, 16}