0=x^2+25x+100

Solution for 0=x^2+25x+100 equation:

Simplifying
0 = x2 + 25x + 100

Reorder the terms:
0 = 100 + 25x + x2

Solving
0 = 100 + 25x + x2

Solving for variable 'x'.

Combine like terms: 0 + -100 = -100
-100 + -25x + -1x2 = 100 + 25x + x2 + -100 + -25x + -1x2

Reorder the terms:
-100 + -25x + -1x2 = 100 + -100 + 25x + -25x + x2 + -1x2

Combine like terms: 100 + -100 = 0
-100 + -25x + -1x2 = 0 + 25x + -25x + x2 + -1x2
-100 + -25x + -1x2 = 25x + -25x + x2 + -1x2

Combine like terms: 25x + -25x = 0
-100 + -25x + -1x2 = 0 + x2 + -1x2
-100 + -25x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-100 + -25x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(100 + 25x + x2) = 0

Factor a trinomial.
-1((20 + x)(5 + x)) = 0

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

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

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

Simplifying
x = -20
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-20, -5}