0=x^2+x-420

Solution for 0=x^2+x-420 equation:

Simplifying
0 = x2 + x + -420

Reorder the terms:
0 = -420 + x + x2

Solving
0 = -420 + x + x2

Solving for variable 'x'.

Combine like terms: 0 + 420 = 420
420 + -1x + -1x2 = -420 + x + x2 + 420 + -1x + -1x2

Reorder the terms:
420 + -1x + -1x2 = -420 + 420 + x + -1x + x2 + -1x2

Combine like terms: -420 + 420 = 0
420 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
420 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
420 + -1x + -1x2 = 0 + x2 + -1x2
420 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
420 + -1x + -1x2 = 0

Factor a trinomial.
(20 + -1x)(21 + x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(21 + x)' equal to zero and attempt to solve:

Simplifying
21 + x = 0

Solving
21 + x = 0

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

Add '-21' to each side of the equation.
21 + -21 + x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + x = 0 + -21
x = 0 + -21

Combine like terms: 0 + -21 = -21
x = -21

Simplifying
x = -21
Solution
x = {20, -21}