(2x+4)(2x+8)=0

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Solution for (2x+4)(2x+8)=0 equation: 


Simplifying
(2x + 4)(2x + 8) = 0

Reorder the terms:
(4 + 2x)(2x + 8) = 0

Reorder the terms:
(4 + 2x)(8 + 2x) = 0

Multiply (4 + 2x) * (8 + 2x)
(4(8 + 2x) + 2x * (8 + 2x)) = 0
((8 * 4 + 2x * 4) + 2x * (8 + 2x)) = 0
((32 + 8x) + 2x * (8 + 2x)) = 0
(32 + 8x + (8 * 2x + 2x * 2x)) = 0
(32 + 8x + (16x + 4x2)) = 0

Combine like terms: 8x + 16x = 24x
(32 + 24x + 4x2) = 0

Solving
32 + 24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 6x + x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-4, -2}

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