10n^2-13n=-6n+6

Solution for 10n^2-13n=-6n+6 equation:

Simplifying
10n2 + -13n = -6n + 6

Reorder the terms:
-13n + 10n2 = -6n + 6

Reorder the terms:
-13n + 10n2 = 6 + -6n

Solving
-13n + 10n2 = 6 + -6n

Solving for variable 'n'.

Reorder the terms:
-6 + -13n + 6n + 10n2 = 6 + -6n + -6 + 6n

Combine like terms: -13n + 6n = -7n
-6 + -7n + 10n2 = 6 + -6n + -6 + 6n

Reorder the terms:
-6 + -7n + 10n2 = 6 + -6 + -6n + 6n

Combine like terms: 6 + -6 = 0
-6 + -7n + 10n2 = 0 + -6n + 6n
-6 + -7n + 10n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
-6 + -7n + 10n2 = 0

Factor a trinomial.
(-1 + -2n)(6 + -5n) = 0

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

Simplifying
-1 + -2n = 0

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

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

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

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-0.5, 1.2}