(2x+6)(2x+8)=0

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Solution for (2x+6)(2x+8)=0 equation: 


Simplifying
(2x + 6)(2x + 8) = 0

Reorder the terms:
(6 + 2x)(2x + 8) = 0

Reorder the terms:
(6 + 2x)(8 + 2x) = 0

Multiply (6 + 2x) * (8 + 2x)
(6(8 + 2x) + 2x * (8 + 2x)) = 0
((8 * 6 + 2x * 6) + 2x * (8 + 2x)) = 0
((48 + 12x) + 2x * (8 + 2x)) = 0
(48 + 12x + (8 * 2x + 2x * 2x)) = 0
(48 + 12x + (16x + 4x2)) = 0

Combine like terms: 12x + 16x = 28x
(48 + 28x + 4x2) = 0

Solving
48 + 28x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 7x + x2) = 0

Factor a trinomial.
4((4 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {-4, -3}

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