(x-6)(3-x)=0

Solution for (x-6)(3-x)=0 equation:

Simplifying
(x + -6)(3 + -1x) = 0

Reorder the terms:
(-6 + x)(3 + -1x) = 0

Multiply (-6 + x) * (3 + -1x)
(-6(3 + -1x) + x(3 + -1x)) = 0
((3 * -6 + -1x * -6) + x(3 + -1x)) = 0
((-18 + 6x) + x(3 + -1x)) = 0
(-18 + 6x + (3 * x + -1x * x)) = 0
(-18 + 6x + (3x + -1x2)) = 0

Combine like terms: 6x + 3x = 9x
(-18 + 9x + -1x2) = 0

Solving
-18 + 9x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 3}