(X-5)(X+9)=15

Solution for (X-5)(X+9)=15 equation:

Simplifying
(X + -5)(X + 9) = 15

Reorder the terms:
(-5 + X)(X + 9) = 15

Reorder the terms:
(-5 + X)(9 + X) = 15

Multiply (-5 + X) * (9 + X)
(-5(9 + X) + X(9 + X)) = 15
((9 * -5 + X * -5) + X(9 + X)) = 15
((-45 + -5X) + X(9 + X)) = 15
(-45 + -5X + (9 * X + X * X)) = 15
(-45 + -5X + (9X + X2)) = 15

Combine like terms: -5X + 9X = 4X
(-45 + 4X + X2) = 15

Solving
-45 + 4X + X2 = 15

Solving for variable 'X'.

Reorder the terms:
-45 + -15 + 4X + X2 = 15 + -15

Combine like terms: -45 + -15 = -60
-60 + 4X + X2 = 15 + -15

Combine like terms: 15 + -15 = 0
-60 + 4X + X2 = 0

Factor a trinomial.
(-10 + -1X)(6 + -1X) = 0

Subproblem 1
Set the factor '(-10 + -1X)' equal to zero and attempt to solve:

Simplifying
-10 + -1X = 0

Solving
-10 + -1X = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1X = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1X = 0 + 10
-1X = 0 + 10

Combine like terms: 0 + 10 = 10
-1X = 10

Divide each side by '-1'.
X = -10

Simplifying
X = -10
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 = {-10, 6}