(12+x)(16+x)=396

Solution for (12+x)(16+x)=396 equation:

Simplifying
(12 + x)(16 + x) = 396

Multiply (12 + x) * (16 + x)
(12(16 + x) + x(16 + x)) = 396
((16 * 12 + x * 12) + x(16 + x)) = 396
((192 + 12x) + x(16 + x)) = 396
(192 + 12x + (16 * x + x * x)) = 396
(192 + 12x + (16x + x2)) = 396

Combine like terms: 12x + 16x = 28x
(192 + 28x + x2) = 396

Solving
192 + 28x + x2 = 396

Solving for variable 'x'.

Reorder the terms:
192 + -396 + 28x + x2 = 396 + -396

Combine like terms: 192 + -396 = -204
-204 + 28x + x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-204 + 28x + x2 = 0

Factor a trinomial.
(-34 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-34, 6}