0=x^2-8x-84

Solution for 0=x^2-8x-84 equation:

Simplifying
0 = x2 + -8x + -84

Reorder the terms:
0 = -84 + -8x + x2

Solving
0 = -84 + -8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 84 = 84
84 + 8x + -1x2 = -84 + -8x + x2 + 84 + 8x + -1x2

Reorder the terms:
84 + 8x + -1x2 = -84 + 84 + -8x + 8x + x2 + -1x2

Combine like terms: -84 + 84 = 0
84 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
84 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
84 + 8x + -1x2 = 0 + x2 + -1x2
84 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
84 + 8x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

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