X^2-8*X-84=0

Solution for X^2-8*X-84=0 equation:

Simplifying
X2 + -8X + -84 = 0

Reorder the terms:
-84 + -8X + X2 = 0

Solving
-84 + -8X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-6 + -1X)(14 + -1X) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(14 + -1X)' equal to zero and attempt to solve:

Simplifying
14 + -1X = 0

Solving
14 + -1X = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1X = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1X = 0 + -14
-1X = 0 + -14

Combine like terms: 0 + -14 = -14
-1X = -14

Divide each side by '-1'.
X = 14

Simplifying
X = 14
Solution
X = {-6, 14}