11n^2-7n-2=-6+8n^2

Solution for 11n^2-7n-2=-6+8n^2 equation:

Simplifying
11n2 + -7n + -2 = -6 + 8n2

Reorder the terms:
-2 + -7n + 11n2 = -6 + 8n2

Solving
-2 + -7n + 11n2 = -6 + 8n2

Solving for variable 'n'.

Reorder the terms:
-2 + 6 + -7n + 11n2 + -8n2 = -6 + 8n2 + 6 + -8n2

Combine like terms: -2 + 6 = 4
4 + -7n + 11n2 + -8n2 = -6 + 8n2 + 6 + -8n2

Combine like terms: 11n2 + -8n2 = 3n2
4 + -7n + 3n2 = -6 + 8n2 + 6 + -8n2

Reorder the terms:
4 + -7n + 3n2 = -6 + 6 + 8n2 + -8n2

Combine like terms: -6 + 6 = 0
4 + -7n + 3n2 = 0 + 8n2 + -8n2
4 + -7n + 3n2 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
4 + -7n + 3n2 = 0

Factor a trinomial.
(1 + -1n)(4 + -3n) = 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 '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {1, 1.333333333}