11n^2+75n-14=36n^2+18n

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Solution for 11n^2+75n-14=36n^2+18n equation: 


Simplifying
11n2 + 75n + -14 = 36n2 + 18n

Reorder the terms:
-14 + 75n + 11n2 = 36n2 + 18n

Reorder the terms:
-14 + 75n + 11n2 = 18n + 36n2

Solving
-14 + 75n + 11n2 = 18n + 36n2

Solving for variable 'n'.

Reorder the terms:
-14 + 75n + -18n + 11n2 + -36n2 = 18n + 36n2 + -18n + -36n2

Combine like terms: 75n + -18n = 57n
-14 + 57n + 11n2 + -36n2 = 18n + 36n2 + -18n + -36n2

Combine like terms: 11n2 + -36n2 = -25n2
-14 + 57n + -25n2 = 18n + 36n2 + -18n + -36n2

Reorder the terms:
-14 + 57n + -25n2 = 18n + -18n + 36n2 + -36n2

Combine like terms: 18n + -18n = 0
-14 + 57n + -25n2 = 0 + 36n2 + -36n2
-14 + 57n + -25n2 = 36n2 + -36n2

Combine like terms: 36n2 + -36n2 = 0
-14 + 57n + -25n2 = 0

Factor a trinomial.
(-2 + n)(7 + -25n) = 0


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

Simplifying
-2 + n = 0

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

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

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

Simplifying
n = 2

Subproblem 2
Set the factor '(7 + -25n)' equal to zero and attempt to solve:

Simplifying
7 + -25n = 0

Solving
7 + -25n = 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 + -25n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -25n = 0 + -7
-25n = 0 + -7

Combine like terms: 0 + -7 = -7
-25n = -7

Divide each side by '-25'.
n = 0.28

Simplifying
n = 0.28
Solution
n = {2, 0.28}

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