(X-5)(X+6)=-18

Solution for (X-5)(X+6)=-18 equation:

Simplifying
(X + -5)(X + 6) = -18

Reorder the terms:
(-5 + X)(X + 6) = -18

Reorder the terms:
(-5 + X)(6 + X) = -18

Multiply (-5 + X) * (6 + X)
(-5(6 + X) + X(6 + X)) = -18
((6 * -5 + X * -5) + X(6 + X)) = -18
((-30 + -5X) + X(6 + X)) = -18
(-30 + -5X + (6 * X + X * X)) = -18
(-30 + -5X + (6X + X2)) = -18

Combine like terms: -5X + 6X = 1X
(-30 + 1X + X2) = -18

Solving
-30 + 1X + X2 = -18

Solving for variable 'X'.

Reorder the terms:
-30 + 18 + 1X + X2 = -18 + 18

Combine like terms: -30 + 18 = -12
-12 + 1X + X2 = -18 + 18

Combine like terms: -18 + 18 = 0
-12 + 1X + X2 = 0

Factor a trinomial.
(-4 + -1X)(3 + -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 '(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 = {-4, 3}