21n^2+14n+7=6n+11

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Solution for 21n^2+14n+7=6n+11 equation: 


Simplifying
21n2 + 14n + 7 = 6n + 11

Reorder the terms:
7 + 14n + 21n2 = 6n + 11

Reorder the terms:
7 + 14n + 21n2 = 11 + 6n

Solving
7 + 14n + 21n2 = 11 + 6n

Solving for variable 'n'.

Reorder the terms:
7 + -11 + 14n + -6n + 21n2 = 11 + 6n + -11 + -6n

Combine like terms: 7 + -11 = -4
-4 + 14n + -6n + 21n2 = 11 + 6n + -11 + -6n

Combine like terms: 14n + -6n = 8n
-4 + 8n + 21n2 = 11 + 6n + -11 + -6n

Reorder the terms:
-4 + 8n + 21n2 = 11 + -11 + 6n + -6n

Combine like terms: 11 + -11 = 0
-4 + 8n + 21n2 = 0 + 6n + -6n
-4 + 8n + 21n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-4 + 8n + 21n2 = 0

Factor a trinomial.
(-2 + -3n)(2 + -7n) = 0


Subproblem 1
Set the factor '(-2 + -3n)' equal to zero and attempt to solve:

Simplifying
-2 + -3n = 0

Solving
-2 + -3n = 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 + -3n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3n = 0 + 2
-3n = 0 + 2

Combine like terms: 0 + 2 = 2
-3n = 2

Divide each side by '-3'.
n = -0.6666666667

Simplifying
n = -0.6666666667

Subproblem 2
Set the factor '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 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 + -7n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Solution
n = {-0.6666666667, 0.2857142857}

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