0=x^2+21x-100

Solution for 0=x^2+21x-100 equation:

Simplifying
0 = x2 + 21x + -100

Reorder the terms:
0 = -100 + 21x + x2

Solving
0 = -100 + 21x + x2

Solving for variable 'x'.

Combine like terms: 0 + 100 = 100
100 + -21x + -1x2 = -100 + 21x + x2 + 100 + -21x + -1x2

Reorder the terms:
100 + -21x + -1x2 = -100 + 100 + 21x + -21x + x2 + -1x2

Combine like terms: -100 + 100 = 0
100 + -21x + -1x2 = 0 + 21x + -21x + x2 + -1x2
100 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
100 + -21x + -1x2 = 0 + x2 + -1x2
100 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
100 + -21x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(25 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25
Solution
x = {4, -25}