(x-9)(x-3)=0

Solution for (x-9)(x-3)=0 equation:

Simplifying
(x + -9)(x + -3) = 0

Reorder the terms:
(-9 + x)(x + -3) = 0

Reorder the terms:
(-9 + x)(-3 + x) = 0

Multiply (-9 + x) * (-3 + x)
(-9(-3 + x) + x(-3 + x)) = 0
((-3 * -9 + x * -9) + x(-3 + x)) = 0
((27 + -9x) + x(-3 + x)) = 0
(27 + -9x + (-3 * x + x * x)) = 0
(27 + -9x + (-3x + x2)) = 0

Combine like terms: -9x + -3x = -12x
(27 + -12x + x2) = 0

Solving
27 + -12x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {3, 9}