21n^2-140n-50=-1

Solution for 21n^2-140n-50=-1 equation:

Simplifying
21n2 + -140n + -50 = -1

Reorder the terms:
-50 + -140n + 21n2 = -1

Solving
-50 + -140n + 21n2 = -1

Solving for variable 'n'.

Reorder the terms:
-50 + 1 + -140n + 21n2 = -1 + 1

Combine like terms: -50 + 1 = -49
-49 + -140n + 21n2 = -1 + 1

Combine like terms: -1 + 1 = 0
-49 + -140n + 21n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + -20n + 3n2) = 0

Factor a trinomial.
7((-1 + -3n)(7 + -1n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve:

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 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 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-0.3333333333, 7}