(2x+4)(2x+4)-2(2x+4)+1=0

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Solution for (2x+4)(2x+4)-2(2x+4)+1=0 equation: 


Simplifying
(2x + 4)(2x + 4) + -2(2x + 4) + 1 = 0

Reorder the terms:
(4 + 2x)(2x + 4) + -2(2x + 4) + 1 = 0

Reorder the terms:
(4 + 2x)(4 + 2x) + -2(2x + 4) + 1 = 0

Multiply (4 + 2x) * (4 + 2x)
(4(4 + 2x) + 2x * (4 + 2x)) + -2(2x + 4) + 1 = 0
((4 * 4 + 2x * 4) + 2x * (4 + 2x)) + -2(2x + 4) + 1 = 0
((16 + 8x) + 2x * (4 + 2x)) + -2(2x + 4) + 1 = 0
(16 + 8x + (4 * 2x + 2x * 2x)) + -2(2x + 4) + 1 = 0
(16 + 8x + (8x + 4x2)) + -2(2x + 4) + 1 = 0

Combine like terms: 8x + 8x = 16x
(16 + 16x + 4x2) + -2(2x + 4) + 1 = 0

Reorder the terms:
16 + 16x + 4x2 + -2(4 + 2x) + 1 = 0
16 + 16x + 4x2 + (4 * -2 + 2x * -2) + 1 = 0
16 + 16x + 4x2 + (-8 + -4x) + 1 = 0

Reorder the terms:
16 + -8 + 1 + 16x + -4x + 4x2 = 0

Combine like terms: 16 + -8 = 8
8 + 1 + 16x + -4x + 4x2 = 0

Combine like terms: 8 + 1 = 9
9 + 16x + -4x + 4x2 = 0

Combine like terms: 16x + -4x = 12x
9 + 12x + 4x2 = 0

Solving
9 + 12x + 4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-1.5, -1.5}

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