6n^2-7n=13

Solution for 6n^2-7n=13 equation:

Simplifying
6n2 + -7n = 13

Reorder the terms:
-7n + 6n2 = 13

Solving
-7n + 6n2 = 13

Solving for variable 'n'.

Reorder the terms:
-13 + -7n + 6n2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -7n + 6n2 = 0

Factor a trinomial.
(-1 + -1n)(13 + -6n) = 0

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

Simplifying
-1 + -1n = 0

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

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(13 + -6n)' equal to zero and attempt to solve:

Simplifying
13 + -6n = 0

Solving
13 + -6n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -6n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -6n = 0 + -13
-6n = 0 + -13

Combine like terms: 0 + -13 = -13
-6n = -13

Divide each side by '-6'.
n = 2.166666667

Simplifying
n = 2.166666667
Solution
n = {-1, 2.166666667}