2n(n+5)=-4(n+5)

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Solution for 2n(n+5)=-4(n+5) equation: 


Simplifying
2n(n + 5) = -4(n + 5)

Reorder the terms:
2n(5 + n) = -4(n + 5)
(5 * 2n + n * 2n) = -4(n + 5)
(10n + 2n2) = -4(n + 5)

Reorder the terms:
10n + 2n2 = -4(5 + n)
10n + 2n2 = (5 * -4 + n * -4)
10n + 2n2 = (-20 + -4n)

Solving
10n + 2n2 = -20 + -4n

Solving for variable 'n'.

Reorder the terms:
20 + 10n + 4n + 2n2 = -20 + -4n + 20 + 4n

Combine like terms: 10n + 4n = 14n
20 + 14n + 2n2 = -20 + -4n + 20 + 4n

Reorder the terms:
20 + 14n + 2n2 = -20 + 20 + -4n + 4n

Combine like terms: -20 + 20 = 0
20 + 14n + 2n2 = 0 + -4n + 4n
20 + 14n + 2n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
20 + 14n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 7n + n2) = 0

Factor a trinomial.
2((5 + n)(2 + n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-5, -2}

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