(x+12)(x+10)=255

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Solution for (x+12)(x+10)=255 equation: 


Simplifying
(x + 12)(x + 10) = 255

Reorder the terms:
(12 + x)(x + 10) = 255

Reorder the terms:
(12 + x)(10 + x) = 255

Multiply (12 + x) * (10 + x)
(12(10 + x) + x(10 + x)) = 255
((10 * 12 + x * 12) + x(10 + x)) = 255
((120 + 12x) + x(10 + x)) = 255
(120 + 12x + (10 * x + x * x)) = 255
(120 + 12x + (10x + x2)) = 255

Combine like terms: 12x + 10x = 22x
(120 + 22x + x2) = 255

Solving
120 + 22x + x2 = 255

Solving for variable 'x'.

Reorder the terms:
120 + -255 + 22x + x2 = 255 + -255

Combine like terms: 120 + -255 = -135
-135 + 22x + x2 = 255 + -255

Combine like terms: 255 + -255 = 0
-135 + 22x + x2 = 0

Factor a trinomial.
(-27 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-27, 5}

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