The value of variable is x = 1.
To solve this problem, we can use the following steps:
Combine the like terms on the left side of the equation:
2x^{2}+2x + x + 5 = 11
2x^{2}+3x + 5 = 11
Subtract 11 from both sides of the equation:
2x^{2}+3x + 5 - 11 = 11 - 11
2x^{2}+3x - 6 = 0
Factor the quadratic expression:
(2x+6)(x-1) = 0
Set each factor equal to zero and solve for x:
2x+6 = 0
x = -3
x-1 = 0
x = 1
Check the solutions by substituting them back into the original equation:
When x = -3:
2(-3)^{2}+2(-3)+x+5 = 11
18-6-3+5 = 11
14 = 11 (Not true)
When x = 1:
2(1)^{2}+2(1)+1+5 = 11
2+2+1+5 = 11
10 = 11 (True)
Therefore, the only solution to the equation is x = 1.