(X-15)(X-22)=0

Solution for (X-15)(X-22)=0 equation:

Simplifying
(X + -15)(X + -22) = 0

Reorder the terms:
(-15 + X)(X + -22) = 0

Reorder the terms:
(-15 + X)(-22 + X) = 0

Multiply (-15 + X) * (-22 + X)
(-15(-22 + X) + X(-22 + X)) = 0
((-22 * -15 + X * -15) + X(-22 + X)) = 0
((330 + -15X) + X(-22 + X)) = 0
(330 + -15X + (-22 * X + X * X)) = 0
(330 + -15X + (-22X + X2)) = 0

Combine like terms: -15X + -22X = -37X
(330 + -37X + X2) = 0

Solving
330 + -37X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(15 + -1X)(22 + -1X) = 0

Subproblem 1
Set the factor '(15 + -1X)' equal to zero and attempt to solve:

Simplifying
15 + -1X = 0

Solving
15 + -1X = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1X = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1X = 0 + -15
-1X = 0 + -15

Combine like terms: 0 + -15 = -15
-1X = -15

Divide each side by '-1'.
X = 15

Simplifying
X = 15
Subproblem 2
Set the factor '(22 + -1X)' equal to zero and attempt to solve:

Simplifying
22 + -1X = 0

Solving
22 + -1X = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1X = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1X = 0 + -22
-1X = 0 + -22

Combine like terms: 0 + -22 = -22
-1X = -22

Divide each side by '-1'.
X = 22

Simplifying
X = 22
Solution
X = {15, 22}