(2x+4)*(2x+4)-3(2x+4)+2=0

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Solution for (2x+4)*(2x+4)-3(2x+4)+2=0 equation: 


Simplifying
(2x + 4)(2x + 4) + -3(2x + 4) + 2 = 0

Reorder the terms:
(4 + 2x)(2x + 4) + -3(2x + 4) + 2 = 0

Reorder the terms:
(4 + 2x)(4 + 2x) + -3(2x + 4) + 2 = 0

Multiply (4 + 2x) * (4 + 2x)
(4(4 + 2x) + 2x * (4 + 2x)) + -3(2x + 4) + 2 = 0
((4 * 4 + 2x * 4) + 2x * (4 + 2x)) + -3(2x + 4) + 2 = 0
((16 + 8x) + 2x * (4 + 2x)) + -3(2x + 4) + 2 = 0
(16 + 8x + (4 * 2x + 2x * 2x)) + -3(2x + 4) + 2 = 0
(16 + 8x + (8x + 4x2)) + -3(2x + 4) + 2 = 0

Combine like terms: 8x + 8x = 16x
(16 + 16x + 4x2) + -3(2x + 4) + 2 = 0

Reorder the terms:
16 + 16x + 4x2 + -3(4 + 2x) + 2 = 0
16 + 16x + 4x2 + (4 * -3 + 2x * -3) + 2 = 0
16 + 16x + 4x2 + (-12 + -6x) + 2 = 0

Reorder the terms:
16 + -12 + 2 + 16x + -6x + 4x2 = 0

Combine like terms: 16 + -12 = 4
4 + 2 + 16x + -6x + 4x2 = 0

Combine like terms: 4 + 2 = 6
6 + 16x + -6x + 4x2 = 0

Combine like terms: 16x + -6x = 10x
6 + 10x + 4x2 = 0

Solving
6 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5x + 2x2) = 0

Factor a trinomial.
2((3 + 2x)(1 + x)) = 0

Ignore the factor 2.

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-1.5, -1}

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