(2x+1)(2x+1)=16

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Solution for (2x+1)(2x+1)=16 equation: 


Simplifying
(2x + 1)(2x + 1) = 16

Reorder the terms:
(1 + 2x)(2x + 1) = 16

Reorder the terms:
(1 + 2x)(1 + 2x) = 16

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 16
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 16
((1 + 2x) + 2x * (1 + 2x)) = 16
(1 + 2x + (1 * 2x + 2x * 2x)) = 16
(1 + 2x + (2x + 4x2)) = 16

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 16

Solving
1 + 4x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
1 + -16 + 4x + 4x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + 4x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + 4x + 4x2 = 0

Factor a trinomial.
(-5 + -2x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2.5, 1.5}

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