(2x+7)(2x+11)=221

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Solution for (2x+7)(2x+11)=221 equation: 


Simplifying
(2x + 7)(2x + 11) = 221

Reorder the terms:
(7 + 2x)(2x + 11) = 221

Reorder the terms:
(7 + 2x)(11 + 2x) = 221

Multiply (7 + 2x) * (11 + 2x)
(7(11 + 2x) + 2x * (11 + 2x)) = 221
((11 * 7 + 2x * 7) + 2x * (11 + 2x)) = 221
((77 + 14x) + 2x * (11 + 2x)) = 221
(77 + 14x + (11 * 2x + 2x * 2x)) = 221
(77 + 14x + (22x + 4x2)) = 221

Combine like terms: 14x + 22x = 36x
(77 + 36x + 4x2) = 221

Solving
77 + 36x + 4x2 = 221

Solving for variable 'x'.

Reorder the terms:
77 + -221 + 36x + 4x2 = 221 + -221

Combine like terms: 77 + -221 = -144
-144 + 36x + 4x2 = 221 + -221

Combine like terms: 221 + -221 = 0
-144 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 9x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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 = {-12, 3}

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