(X+2)(X-9)=-24

Solution for (X+2)(X-9)=-24 equation:

Simplifying
(X + 2)(X + -9) = -24

Reorder the terms:
(2 + X)(X + -9) = -24

Reorder the terms:
(2 + X)(-9 + X) = -24

Multiply (2 + X) * (-9 + X)
(2(-9 + X) + X(-9 + X)) = -24
((-9 * 2 + X * 2) + X(-9 + X)) = -24
((-18 + 2X) + X(-9 + X)) = -24
(-18 + 2X + (-9 * X + X * X)) = -24
(-18 + 2X + (-9X + X2)) = -24

Combine like terms: 2X + -9X = -7X
(-18 + -7X + X2) = -24

Solving
-18 + -7X + X2 = -24

Solving for variable 'X'.

Reorder the terms:
-18 + 24 + -7X + X2 = -24 + 24

Combine like terms: -18 + 24 = 6
6 + -7X + X2 = -24 + 24

Combine like terms: -24 + 24 = 0
6 + -7X + X2 = 0

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

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
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 = {1, 6}