15-21n=-5n^2+1-4n

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Solution for 15-21n=-5n^2+1-4n equation: 


Simplifying
15 + -21n = -5n2 + 1 + -4n

Reorder the terms:
15 + -21n = 1 + -4n + -5n2

Solving
15 + -21n = 1 + -4n + -5n2

Solving for variable 'n'.

Reorder the terms:
15 + -1 + -21n + 4n + 5n2 = 1 + -4n + -5n2 + -1 + 4n + 5n2

Combine like terms: 15 + -1 = 14
14 + -21n + 4n + 5n2 = 1 + -4n + -5n2 + -1 + 4n + 5n2

Combine like terms: -21n + 4n = -17n
14 + -17n + 5n2 = 1 + -4n + -5n2 + -1 + 4n + 5n2

Reorder the terms:
14 + -17n + 5n2 = 1 + -1 + -4n + 4n + -5n2 + 5n2

Combine like terms: 1 + -1 = 0
14 + -17n + 5n2 = 0 + -4n + 4n + -5n2 + 5n2
14 + -17n + 5n2 = -4n + 4n + -5n2 + 5n2

Combine like terms: -4n + 4n = 0
14 + -17n + 5n2 = 0 + -5n2 + 5n2
14 + -17n + 5n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
14 + -17n + 5n2 = 0

Factor a trinomial.
(7 + -5n)(2 + -1n) = 0


Subproblem 1
Set the factor '(7 + -5n)' equal to zero and attempt to solve:

Simplifying
7 + -5n = 0

Solving
7 + -5n = 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 + -5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5n = 0 + -7
-5n = 0 + -7

Combine like terms: 0 + -7 = -7
-5n = -7

Divide each side by '-5'.
n = 1.4

Simplifying
n = 1.4

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {1.4, 2}

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