(x+18)(x+9)=400

Solution for (x+18)(x+9)=400 equation:

Simplifying
(x + 18)(x + 9) = 400

Reorder the terms:
(18 + x)(x + 9) = 400

Reorder the terms:
(18 + x)(9 + x) = 400

Multiply (18 + x) * (9 + x)
(18(9 + x) + x(9 + x)) = 400
((9 * 18 + x * 18) + x(9 + x)) = 400
((162 + 18x) + x(9 + x)) = 400
(162 + 18x + (9 * x + x * x)) = 400
(162 + 18x + (9x + x2)) = 400

Combine like terms: 18x + 9x = 27x
(162 + 27x + x2) = 400

Solving
162 + 27x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
162 + -400 + 27x + x2 = 400 + -400

Combine like terms: 162 + -400 = -238
-238 + 27x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-238 + 27x + x2 = 0

Factor a trinomial.
(-34 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-34, 7}