(x+6)(x+3)=238

Solution for (x+6)(x+3)=238 equation:

Simplifying
(x + 6)(x + 3) = 238

Reorder the terms:
(6 + x)(x + 3) = 238

Reorder the terms:
(6 + x)(3 + x) = 238

Multiply (6 + x) * (3 + x)
(6(3 + x) + x(3 + x)) = 238
((3 * 6 + x * 6) + x(3 + x)) = 238
((18 + 6x) + x(3 + x)) = 238
(18 + 6x + (3 * x + x * x)) = 238
(18 + 6x + (3x + x2)) = 238

Combine like terms: 6x + 3x = 9x
(18 + 9x + x2) = 238

Solving
18 + 9x + x2 = 238

Solving for variable 'x'.

Reorder the terms:
18 + -238 + 9x + x2 = 238 + -238

Combine like terms: 18 + -238 = -220
-220 + 9x + x2 = 238 + -238

Combine like terms: 238 + -238 = 0
-220 + 9x + x2 = 0

Factor a trinomial.
(-20 + -1x)(11 + -1x) = 0

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

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 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 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-20, 11}