3(n^2-15)+4n=4n(n-3)+19

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Solution for 3(n^2-15)+4n=4n(n-3)+19 equation: 


Simplifying
3(n2 + -15) + 4n = 4n(n + -3) + 19

Reorder the terms:
3(-15 + n2) + 4n = 4n(n + -3) + 19
(-15 * 3 + n2 * 3) + 4n = 4n(n + -3) + 19
(-45 + 3n2) + 4n = 4n(n + -3) + 19

Reorder the terms:
-45 + 4n + 3n2 = 4n(n + -3) + 19

Reorder the terms:
-45 + 4n + 3n2 = 4n(-3 + n) + 19
-45 + 4n + 3n2 = (-3 * 4n + n * 4n) + 19
-45 + 4n + 3n2 = (-12n + 4n2) + 19

Reorder the terms:
-45 + 4n + 3n2 = 19 + -12n + 4n2

Solving
-45 + 4n + 3n2 = 19 + -12n + 4n2

Solving for variable 'n'.

Reorder the terms:
-45 + -19 + 4n + 12n + 3n2 + -4n2 = 19 + -12n + 4n2 + -19 + 12n + -4n2

Combine like terms: -45 + -19 = -64
-64 + 4n + 12n + 3n2 + -4n2 = 19 + -12n + 4n2 + -19 + 12n + -4n2

Combine like terms: 4n + 12n = 16n
-64 + 16n + 3n2 + -4n2 = 19 + -12n + 4n2 + -19 + 12n + -4n2

Combine like terms: 3n2 + -4n2 = -1n2
-64 + 16n + -1n2 = 19 + -12n + 4n2 + -19 + 12n + -4n2

Reorder the terms:
-64 + 16n + -1n2 = 19 + -19 + -12n + 12n + 4n2 + -4n2

Combine like terms: 19 + -19 = 0
-64 + 16n + -1n2 = 0 + -12n + 12n + 4n2 + -4n2
-64 + 16n + -1n2 = -12n + 12n + 4n2 + -4n2

Combine like terms: -12n + 12n = 0
-64 + 16n + -1n2 = 0 + 4n2 + -4n2
-64 + 16n + -1n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-64 + 16n + -1n2 = 0

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


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

Simplifying
-8 + n = 0

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

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

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

Simplifying
n = 8

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 = {8, 8}

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