0=x(x+21)

Solution for 0=x(x+21) equation:

Simplifying
0 = x(x + 21)

Reorder the terms:
0 = x(21 + x)
0 = (21 * x + x * x)
0 = (21x + x2)

Solving
0 = 21x + x2

Solving for variable 'x'.
Remove the zero:
-21x + -1x2 = 21x + x2 + -21x + -1x2

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

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

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

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(21 + x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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 = {0, -21}