(x+11)(2x+5)=117

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Solution for (x+11)(2x+5)=117 equation: 


Simplifying
(x + 11)(2x + 5) = 117

Reorder the terms:
(11 + x)(2x + 5) = 117

Reorder the terms:
(11 + x)(5 + 2x) = 117

Multiply (11 + x) * (5 + 2x)
(11(5 + 2x) + x(5 + 2x)) = 117
((5 * 11 + 2x * 11) + x(5 + 2x)) = 117
((55 + 22x) + x(5 + 2x)) = 117
(55 + 22x + (5 * x + 2x * x)) = 117
(55 + 22x + (5x + 2x2)) = 117

Combine like terms: 22x + 5x = 27x
(55 + 27x + 2x2) = 117

Solving
55 + 27x + 2x2 = 117

Solving for variable 'x'.

Reorder the terms:
55 + -117 + 27x + 2x2 = 117 + -117

Combine like terms: 55 + -117 = -62
-62 + 27x + 2x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-62 + 27x + 2x2 = 0

Factor a trinomial.
(-31 + -2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-31 + -2x)' equal to zero and attempt to solve:

Simplifying
-31 + -2x = 0

Solving
-31 + -2x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2x = 0 + 31
-2x = 0 + 31

Combine like terms: 0 + 31 = 31
-2x = 31

Divide each side by '-2'.
x = -15.5

Simplifying
x = -15.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15.5, 2}

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