9n^2+151=4+84n

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Solution for 9n^2+151=4+84n equation: 


Simplifying
9n2 + 151 = 4 + 84n

Reorder the terms:
151 + 9n2 = 4 + 84n

Solving
151 + 9n2 = 4 + 84n

Solving for variable 'n'.

Reorder the terms:
151 + -4 + -84n + 9n2 = 4 + 84n + -4 + -84n

Combine like terms: 151 + -4 = 147
147 + -84n + 9n2 = 4 + 84n + -4 + -84n

Reorder the terms:
147 + -84n + 9n2 = 4 + -4 + 84n + -84n

Combine like terms: 4 + -4 = 0
147 + -84n + 9n2 = 0 + 84n + -84n
147 + -84n + 9n2 = 84n + -84n

Combine like terms: 84n + -84n = 0
147 + -84n + 9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(49 + -28n + 3n2) = 0

Factor a trinomial.
3((7 + -3n)(7 + -1n)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -3n)' equal to zero and attempt to solve:

Simplifying
7 + -3n = 0

Solving
7 + -3n = 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 + -3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3n = 0 + -7
-3n = 0 + -7

Combine like terms: 0 + -7 = -7
-3n = -7

Divide each side by '-3'.
n = 2.333333333

Simplifying
n = 2.333333333

Subproblem 2
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
Solution
n = {2.333333333, 7}

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