(2x+1)(2x+1)=x+11

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Solution for (2x+1)(2x+1)=x+11 equation: 


Simplifying
(2x + 1)(2x + 1) = x + 11

Reorder the terms:
(1 + 2x)(2x + 1) = x + 11

Reorder the terms:
(1 + 2x)(1 + 2x) = x + 11

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = x + 11
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = x + 11
((1 + 2x) + 2x * (1 + 2x)) = x + 11
(1 + 2x + (1 * 2x + 2x * 2x)) = x + 11
(1 + 2x + (2x + 4x2)) = x + 11

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = x + 11

Reorder the terms:
1 + 4x + 4x2 = 11 + x

Solving
1 + 4x + 4x2 = 11 + x

Solving for variable 'x'.

Reorder the terms:
1 + -11 + 4x + -1x + 4x2 = 11 + x + -11 + -1x

Combine like terms: 1 + -11 = -10
-10 + 4x + -1x + 4x2 = 11 + x + -11 + -1x

Combine like terms: 4x + -1x = 3x
-10 + 3x + 4x2 = 11 + x + -11 + -1x

Reorder the terms:
-10 + 3x + 4x2 = 11 + -11 + x + -1x

Combine like terms: 11 + -11 = 0
-10 + 3x + 4x2 = 0 + x + -1x
-10 + 3x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-10 + 3x + 4x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-2, 1.25}

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