(12+x)(14+x)=255

Solution for (12+x)(14+x)=255 equation:

Simplifying
(12 + x)(14 + x) = 255

Multiply (12 + x) * (14 + x)
(12(14 + x) + x(14 + x)) = 255
((14 * 12 + x * 12) + x(14 + x)) = 255
((168 + 12x) + x(14 + x)) = 255
(168 + 12x + (14 * x + x * x)) = 255
(168 + 12x + (14x + x2)) = 255

Combine like terms: 12x + 14x = 26x
(168 + 26x + x2) = 255

Solving
168 + 26x + x2 = 255

Solving for variable 'x'.

Reorder the terms:
168 + -255 + 26x + x2 = 255 + -255

Combine like terms: 168 + -255 = -87
-87 + 26x + x2 = 255 + -255

Combine like terms: 255 + -255 = 0
-87 + 26x + x2 = 0

Factor a trinomial.
(-29 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-29 + -1x)' equal to zero and attempt to solve:

Simplifying
-29 + -1x = 0

Solving
-29 + -1x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1x = 0 + 29
-1x = 0 + 29

Combine like terms: 0 + 29 = 29
-1x = 29

Divide each side by '-1'.
x = -29

Simplifying
x = -29
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-29, 3}