16n(n+7)=4(28+4n)

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Solution for 16n(n+7)=4(28+4n) equation: 


Simplifying
16n(n + 7) = 4(28 + 4n)

Reorder the terms:
16n(7 + n) = 4(28 + 4n)
(7 * 16n + n * 16n) = 4(28 + 4n)
(112n + 16n2) = 4(28 + 4n)
112n + 16n2 = (28 * 4 + 4n * 4)
112n + 16n2 = (112 + 16n)

Solving
112n + 16n2 = 112 + 16n

Solving for variable 'n'.

Reorder the terms:
-112 + 112n + -16n + 16n2 = 112 + 16n + -112 + -16n

Combine like terms: 112n + -16n = 96n
-112 + 96n + 16n2 = 112 + 16n + -112 + -16n

Reorder the terms:
-112 + 96n + 16n2 = 112 + -112 + 16n + -16n

Combine like terms: 112 + -112 = 0
-112 + 96n + 16n2 = 0 + 16n + -16n
-112 + 96n + 16n2 = 16n + -16n

Combine like terms: 16n + -16n = 0
-112 + 96n + 16n2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-7 + 6n + n2) = 0

Factor a trinomial.
16((-7 + -1n)(1 + -1n)) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7

Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-7, 1}

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