7n^2-21n+1=-5n-3

Solution for 7n^2-21n+1=-5n-3 equation:

Simplifying
7n2 + -21n + 1 = -5n + -3

Reorder the terms:
1 + -21n + 7n2 = -5n + -3

Reorder the terms:
1 + -21n + 7n2 = -3 + -5n

Solving
1 + -21n + 7n2 = -3 + -5n

Solving for variable 'n'.

Reorder the terms:
1 + 3 + -21n + 5n + 7n2 = -3 + -5n + 3 + 5n

Combine like terms: 1 + 3 = 4
4 + -21n + 5n + 7n2 = -3 + -5n + 3 + 5n

Combine like terms: -21n + 5n = -16n
4 + -16n + 7n2 = -3 + -5n + 3 + 5n

Reorder the terms:
4 + -16n + 7n2 = -3 + 3 + -5n + 5n

Combine like terms: -3 + 3 = 0
4 + -16n + 7n2 = 0 + -5n + 5n
4 + -16n + 7n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
4 + -16n + 7n2 = 0

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

Subproblem 1
Set the factor '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 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 + -7n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
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 = {0.2857142857, 2}