(X-6)(X-3)=

Solution for (X-6)(X-3)= equation:

Simplifying
(X + -6)(X + -3) = 0

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

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

Multiply (-6 + X) * (-3 + X)
(-6(-3 + X) + X(-3 + X)) = 0
((-3 * -6 + X * -6) + X(-3 + X)) = 0
((18 + -6X) + X(-3 + X)) = 0
(18 + -6X + (-3 * X + X * X)) = 0
(18 + -6X + (-3X + X2)) = 0

Combine like terms: -6X + -3X = -9X
(18 + -9X + X2) = 0

Solving
18 + -9X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(3 + -1X)(6 + -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 '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 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 + -1X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X = 0 + -6
-1X = 0 + -6

Combine like terms: 0 + -6 = -6
-1X = -6

Divide each side by '-1'.
X = 6

Simplifying
X = 6
Solution
X = {3, 6}