0=x^2+84x+164

Solution for 0=x^2+84x+164 equation:

Simplifying
0 = x2 + 84x + 164

Reorder the terms:
0 = 164 + 84x + x2

Solving
0 = 164 + 84x + x2

Solving for variable 'x'.

Combine like terms: 0 + -164 = -164
-164 + -84x + -1x2 = 164 + 84x + x2 + -164 + -84x + -1x2

Reorder the terms:
-164 + -84x + -1x2 = 164 + -164 + 84x + -84x + x2 + -1x2

Combine like terms: 164 + -164 = 0
-164 + -84x + -1x2 = 0 + 84x + -84x + x2 + -1x2
-164 + -84x + -1x2 = 84x + -84x + x2 + -1x2

Combine like terms: 84x + -84x = 0
-164 + -84x + -1x2 = 0 + x2 + -1x2
-164 + -84x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-164 + -84x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(164 + 84x + x2) = 0

Factor a trinomial.
-1((82 + x)(2 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(82 + x)' equal to zero and attempt to solve:

Simplifying
82 + x = 0

Solving
82 + x = 0

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

Add '-82' to each side of the equation.
82 + -82 + x = 0 + -82

Combine like terms: 82 + -82 = 0
0 + x = 0 + -82
x = 0 + -82

Combine like terms: 0 + -82 = -82
x = -82

Simplifying
x = -82
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-82, -2}