37n^2-51n-13=2n^2-5

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Solution for 37n^2-51n-13=2n^2-5 equation: 


Simplifying
37n2 + -51n + -13 = 2n2 + -5

Reorder the terms:
-13 + -51n + 37n2 = 2n2 + -5

Reorder the terms:
-13 + -51n + 37n2 = -5 + 2n2

Solving
-13 + -51n + 37n2 = -5 + 2n2

Solving for variable 'n'.

Reorder the terms:
-13 + 5 + -51n + 37n2 + -2n2 = -5 + 2n2 + 5 + -2n2

Combine like terms: -13 + 5 = -8
-8 + -51n + 37n2 + -2n2 = -5 + 2n2 + 5 + -2n2

Combine like terms: 37n2 + -2n2 = 35n2
-8 + -51n + 35n2 = -5 + 2n2 + 5 + -2n2

Reorder the terms:
-8 + -51n + 35n2 = -5 + 5 + 2n2 + -2n2

Combine like terms: -5 + 5 = 0
-8 + -51n + 35n2 = 0 + 2n2 + -2n2
-8 + -51n + 35n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-8 + -51n + 35n2 = 0

Factor a trinomial.
(-1 + -7n)(8 + -5n) = 0


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

Simplifying
-1 + -7n = 0

Solving
-1 + -7n = 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 + -7n = 0 + 1

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

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

Divide each side by '-7'.
n = -0.1428571429

Simplifying
n = -0.1428571429

Subproblem 2
Set the factor '(8 + -5n)' equal to zero and attempt to solve:

Simplifying
8 + -5n = 0

Solving
8 + -5n = 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 + -5n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5n = 0 + -8
-5n = 0 + -8

Combine like terms: 0 + -8 = -8
-5n = -8

Divide each side by '-5'.
n = 1.6

Simplifying
n = 1.6
Solution
n = {-0.1428571429, 1.6}

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