0=(x+21)(x-5)

Solution for 0=(x+21)(x-5) equation:

Simplifying
0 = (x + 21)(x + -5)

Reorder the terms:
0 = (21 + x)(x + -5)

Reorder the terms:
0 = (21 + x)(-5 + x)

Multiply (21 + x) * (-5 + x)
0 = (21(-5 + x) + x(-5 + x))
0 = ((-5 * 21 + x * 21) + x(-5 + x))
0 = ((-105 + 21x) + x(-5 + x))
0 = (-105 + 21x + (-5 * x + x * x))
0 = (-105 + 21x + (-5x + x2))

Combine like terms: 21x + -5x = 16x
0 = (-105 + 16x + x2)

Solving
0 = -105 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + 105 = 105
105 + -16x + -1x2 = -105 + 16x + x2 + 105 + -16x + -1x2

Reorder the terms:
105 + -16x + -1x2 = -105 + 105 + 16x + -16x + x2 + -1x2

Combine like terms: -105 + 105 = 0
105 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
105 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
105 + -16x + -1x2 = 0 + x2 + -1x2
105 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
105 + -16x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(21 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
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 = {5, -21}