21n^2+107n+105=-7-5n

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Solution for 21n^2+107n+105=-7-5n equation: 


Simplifying
21n2 + 107n + 105 = -7 + -5n

Reorder the terms:
105 + 107n + 21n2 = -7 + -5n

Solving
105 + 107n + 21n2 = -7 + -5n

Solving for variable 'n'.

Reorder the terms:
105 + 7 + 107n + 5n + 21n2 = -7 + -5n + 7 + 5n

Combine like terms: 105 + 7 = 112
112 + 107n + 5n + 21n2 = -7 + -5n + 7 + 5n

Combine like terms: 107n + 5n = 112n
112 + 112n + 21n2 = -7 + -5n + 7 + 5n

Reorder the terms:
112 + 112n + 21n2 = -7 + 7 + -5n + 5n

Combine like terms: -7 + 7 = 0
112 + 112n + 21n2 = 0 + -5n + 5n
112 + 112n + 21n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
112 + 112n + 21n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(16 + 16n + 3n2) = 0

Factor a trinomial.
7((4 + n)(4 + 3n)) = 0

Ignore the factor 7.

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

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

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

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

Simplifying
n = -4

Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Solution
n = {-4, -1.333333333}

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