(X-3)(X+6)=

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

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

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

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

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

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

Solving
-18 + 3X + X2 = 0

Solving for variable 'X'.

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

Subproblem 1
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
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}