(2n+2)(2n+6)=

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Solution for (2n+2)(2n+6)= equation:


Simplifying
(2n + 2)(2n + 6) = 0

Reorder the terms:
(2 + 2n)(2n + 6) = 0

Reorder the terms:
(2 + 2n)(6 + 2n) = 0

Multiply (2 + 2n) * (6 + 2n)
(2(6 + 2n) + 2n * (6 + 2n)) = 0
((6 * 2 + 2n * 2) + 2n * (6 + 2n)) = 0
((12 + 4n) + 2n * (6 + 2n)) = 0
(12 + 4n + (6 * 2n + 2n * 2n)) = 0
(12 + 4n + (12n + 4n2)) = 0

Combine like terms: 4n + 12n = 16n
(12 + 16n + 4n2) = 0

Solving
12 + 16n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 4n + n2) = 0

Factor a trinomial.
4((3 + n)(1 + n)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3

Subproblem 2

Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1

Solution

n = {-3, -1}

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