80x+x^2=164

Solution for 80x+x^2=164 equation:

Simplifying
80x + x2 = 164

Solving
80x + x2 = 164

Solving for variable 'x'.

Reorder the terms:
-164 + 80x + x2 = 164 + -164

Combine like terms: 164 + -164 = 0
-164 + 80x + x2 = 0

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

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

Simplifying
-82 + -1x = 0

Solving
-82 + -1x = 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 + -1x = 0 + 82

Combine like terms: -82 + 82 = 0
0 + -1x = 0 + 82
-1x = 0 + 82

Combine like terms: 0 + 82 = 82
-1x = 82

Divide each side by '-1'.
x = -82

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