(x-3)(16-x)=0

Solution for (x-3)(16-x)=0 equation:

Simplifying
(x + -3)(16 + -1x) = 0

Reorder the terms:
(-3 + x)(16 + -1x) = 0

Multiply (-3 + x) * (16 + -1x)
(-3(16 + -1x) + x(16 + -1x)) = 0
((16 * -3 + -1x * -3) + x(16 + -1x)) = 0
((-48 + 3x) + x(16 + -1x)) = 0
(-48 + 3x + (16 * x + -1x * x)) = 0
(-48 + 3x + (16x + -1x2)) = 0

Combine like terms: 3x + 16x = 19x
(-48 + 19x + -1x2) = 0

Solving
-48 + 19x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-16 + x)(3 + -1x) = 0

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

Simplifying
-16 + x = 0

Solving
-16 + x = 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 + x = 0 + 16

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

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

Simplifying
x = 16
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {16, 3}