(x+2)(x+5)=208

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Solution for (x+2)(x+5)=208 equation: 


Simplifying
(x + 2)(x + 5) = 208

Reorder the terms:
(2 + x)(x + 5) = 208

Reorder the terms:
(2 + x)(5 + x) = 208

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) = 208
((5 * 2 + x * 2) + x(5 + x)) = 208
((10 + 2x) + x(5 + x)) = 208
(10 + 2x + (5 * x + x * x)) = 208
(10 + 2x + (5x + x2)) = 208

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) = 208

Solving
10 + 7x + x2 = 208

Solving for variable 'x'.

Reorder the terms:
10 + -208 + 7x + x2 = 208 + -208

Combine like terms: 10 + -208 = -198
-198 + 7x + x2 = 208 + -208

Combine like terms: 208 + -208 = 0
-198 + 7x + x2 = 0

Factor a trinomial.
(-18 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-18, 11}

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