(2x+5)(2x+6)=272

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Solution for (2x+5)(2x+6)=272 equation: 


Simplifying
(2x + 5)(2x + 6) = 272

Reorder the terms:
(5 + 2x)(2x + 6) = 272

Reorder the terms:
(5 + 2x)(6 + 2x) = 272

Multiply (5 + 2x) * (6 + 2x)
(5(6 + 2x) + 2x * (6 + 2x)) = 272
((6 * 5 + 2x * 5) + 2x * (6 + 2x)) = 272
((30 + 10x) + 2x * (6 + 2x)) = 272
(30 + 10x + (6 * 2x + 2x * 2x)) = 272
(30 + 10x + (12x + 4x2)) = 272

Combine like terms: 10x + 12x = 22x
(30 + 22x + 4x2) = 272

Solving
30 + 22x + 4x2 = 272

Solving for variable 'x'.

Reorder the terms:
30 + -272 + 22x + 4x2 = 272 + -272

Combine like terms: 30 + -272 = -242
-242 + 22x + 4x2 = 272 + -272

Combine like terms: 272 + -272 = 0
-242 + 22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-121 + 11x + 2x2) = 0

Factor a trinomial.
2((-11 + -1x)(11 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
11 + -2x = 0

Solving
11 + -2x = 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 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-11, 5.5}

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