14n^2-67n+52=4+7n^2-5n

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Solution for 14n^2-67n+52=4+7n^2-5n equation: 


Simplifying
14n2 + -67n + 52 = 4 + 7n2 + -5n

Reorder the terms:
52 + -67n + 14n2 = 4 + 7n2 + -5n

Reorder the terms:
52 + -67n + 14n2 = 4 + -5n + 7n2

Solving
52 + -67n + 14n2 = 4 + -5n + 7n2

Solving for variable 'n'.

Reorder the terms:
52 + -4 + -67n + 5n + 14n2 + -7n2 = 4 + -5n + 7n2 + -4 + 5n + -7n2

Combine like terms: 52 + -4 = 48
48 + -67n + 5n + 14n2 + -7n2 = 4 + -5n + 7n2 + -4 + 5n + -7n2

Combine like terms: -67n + 5n = -62n
48 + -62n + 14n2 + -7n2 = 4 + -5n + 7n2 + -4 + 5n + -7n2

Combine like terms: 14n2 + -7n2 = 7n2
48 + -62n + 7n2 = 4 + -5n + 7n2 + -4 + 5n + -7n2

Reorder the terms:
48 + -62n + 7n2 = 4 + -4 + -5n + 5n + 7n2 + -7n2

Combine like terms: 4 + -4 = 0
48 + -62n + 7n2 = 0 + -5n + 5n + 7n2 + -7n2
48 + -62n + 7n2 = -5n + 5n + 7n2 + -7n2

Combine like terms: -5n + 5n = 0
48 + -62n + 7n2 = 0 + 7n2 + -7n2
48 + -62n + 7n2 = 7n2 + -7n2

Combine like terms: 7n2 + -7n2 = 0
48 + -62n + 7n2 = 0

Factor a trinomial.
(6 + -7n)(8 + -1n) = 0


Subproblem 1
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571

Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {0.8571428571, 8}

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