(X-13)(X+53)=0

Solution for (X-13)(X+53)=0 equation:

Simplifying
(X + -13)(X + 53) = 0

Reorder the terms:
(-13 + X)(X + 53) = 0

Reorder the terms:
(-13 + X)(53 + X) = 0

Multiply (-13 + X) * (53 + X)
(-13(53 + X) + X(53 + X)) = 0
((53 * -13 + X * -13) + X(53 + X)) = 0
((-689 + -13X) + X(53 + X)) = 0
(-689 + -13X + (53 * X + X * X)) = 0
(-689 + -13X + (53X + X2)) = 0

Combine like terms: -13X + 53X = 40X
(-689 + 40X + X2) = 0

Solving
-689 + 40X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-53 + -1X)(13 + -1X) = 0

Subproblem 1
Set the factor '(-53 + -1X)' equal to zero and attempt to solve:

Simplifying
-53 + -1X = 0

Solving
-53 + -1X = 0

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

Add '53' to each side of the equation.
-53 + 53 + -1X = 0 + 53

Combine like terms: -53 + 53 = 0
0 + -1X = 0 + 53
-1X = 0 + 53

Combine like terms: 0 + 53 = 53
-1X = 53

Divide each side by '-1'.
X = -53

Simplifying
X = -53
Subproblem 2
Set the factor '(13 + -1X)' equal to zero and attempt to solve:

Simplifying
13 + -1X = 0

Solving
13 + -1X = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1X = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1X = 0 + -13
-1X = 0 + -13

Combine like terms: 0 + -13 = -13
-1X = -13

Divide each side by '-1'.
X = 13

Simplifying
X = 13
Solution
X = {-53, 13}