(x+21)(x-3)=0

Solution for (x+21)(x-3)=0 equation:

Simplifying
(x + 21)(x + -3) = 0

Reorder the terms:
(21 + x)(x + -3) = 0

Reorder the terms:
(21 + x)(-3 + x) = 0

Multiply (21 + x) * (-3 + x)
(21(-3 + x) + x(-3 + x)) = 0
((-3 * 21 + x * 21) + x(-3 + x)) = 0
((-63 + 21x) + x(-3 + x)) = 0
(-63 + 21x + (-3 * x + x * x)) = 0
(-63 + 21x + (-3x + x2)) = 0

Combine like terms: 21x + -3x = 18x
(-63 + 18x + x2) = 0

Solving
-63 + 18x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-21 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 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 + -1x = 0 + 21

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

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

Divide each side by '-1'.
x = -21

Simplifying
x = -21
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-21, 3}