(x-9)(x-4)=0

Solution for (x-9)(x-4)=0 equation:

Simplifying
(x + -9)(x + -4) = 0

Reorder the terms:
(-9 + x)(x + -4) = 0

Reorder the terms:
(-9 + x)(-4 + x) = 0

Multiply (-9 + x) * (-4 + x)
(-9(-4 + x) + x(-4 + x)) = 0
((-4 * -9 + x * -9) + x(-4 + x)) = 0
((36 + -9x) + x(-4 + x)) = 0
(36 + -9x + (-4 * x + x * x)) = 0
(36 + -9x + (-4x + x2)) = 0

Combine like terms: -9x + -4x = -13x
(36 + -13x + x2) = 0

Solving
36 + -13x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, 9}