13X^2-52X-156=0

Solution for 13X^2-52X-156=0 equation:

Simplifying
13X2 + -52X + -156 = 0

Reorder the terms:
-156 + -52X + 13X2 = 0

Solving
-156 + -52X + 13X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '13'.
13(-12 + -4X + X2) = 0

Factor a trinomial.
13((-2 + -1X)(6 + -1X)) = 0

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

Simplifying
-2 + -1X = 0

Solving
-2 + -1X = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1X = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1X = 0 + 2
-1X = 0 + 2

Combine like terms: 0 + 2 = 2
-1X = 2

Divide each side by '-1'.
X = -2

Simplifying
X = -2
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 = {-2, 6}