4n^2-6n-80=-10

Solution for 4n^2-6n-80=-10 equation:

Simplifying
4n2 + -6n + -80 = -10

Reorder the terms:
-80 + -6n + 4n2 = -10

Solving
-80 + -6n + 4n2 = -10

Solving for variable 'n'.

Reorder the terms:
-80 + 10 + -6n + 4n2 = -10 + 10

Combine like terms: -80 + 10 = -70
-70 + -6n + 4n2 = -10 + 10

Combine like terms: -10 + 10 = 0
-70 + -6n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -3n + 2n2) = 0

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

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

Simplifying
-7 + -2n = 0

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

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

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

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-3.5, 5}