(x+2)(x+6)=21

Solution for (x+2)(x+6)=21 equation:

Simplifying
(x + 2)(x + 6) = 21

Reorder the terms:
(2 + x)(x + 6) = 21

Reorder the terms:
(2 + x)(6 + x) = 21

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = 21
((6 * 2 + x * 2) + x(6 + x)) = 21
((12 + 2x) + x(6 + x)) = 21
(12 + 2x + (6 * x + x * x)) = 21
(12 + 2x + (6x + x2)) = 21

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = 21

Solving
12 + 8x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
12 + -21 + 8x + x2 = 21 + -21

Combine like terms: 12 + -21 = -9
-9 + 8x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-9 + 8x + x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-9, 1}