(X+3)(X+8)=234

Solution for (X+3)(X+8)=234 equation:

Simplifying
(X + 3)(X + 8) = 234

Reorder the terms:
(3 + X)(X + 8) = 234

Reorder the terms:
(3 + X)(8 + X) = 234

Multiply (3 + X) * (8 + X)
(3(8 + X) + X(8 + X)) = 234
((8 * 3 + X * 3) + X(8 + X)) = 234
((24 + 3X) + X(8 + X)) = 234
(24 + 3X + (8 * X + X * X)) = 234
(24 + 3X + (8X + X2)) = 234

Combine like terms: 3X + 8X = 11X
(24 + 11X + X2) = 234

Solving
24 + 11X + X2 = 234

Solving for variable 'X'.

Reorder the terms:
24 + -234 + 11X + X2 = 234 + -234

Combine like terms: 24 + -234 = -210
-210 + 11X + X2 = 234 + -234

Combine like terms: 234 + -234 = 0
-210 + 11X + X2 = 0

Factor a trinomial.
(-21 + -1X)(10 + -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 '(10 + -1X)' equal to zero and attempt to solve:

Simplifying
10 + -1X = 0

Solving
10 + -1X = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1X = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1X = 0 + -10
-1X = 0 + -10

Combine like terms: 0 + -10 = -10
-1X = -10

Divide each side by '-1'.
X = 10

Simplifying
X = 10
Solution
X = {-21, 10}