8n^2-15n=-2+n^2

Solution for 8n^2-15n=-2+n^2 equation:

Simplifying
8n2 + -15n = -2 + n2

Reorder the terms:
-15n + 8n2 = -2 + n2

Solving
-15n + 8n2 = -2 + n2

Solving for variable 'n'.

Reorder the terms:
2 + -15n + 8n2 + -1n2 = -2 + n2 + 2 + -1n2

Combine like terms: 8n2 + -1n2 = 7n2
2 + -15n + 7n2 = -2 + n2 + 2 + -1n2

Reorder the terms:
2 + -15n + 7n2 = -2 + 2 + n2 + -1n2

Combine like terms: -2 + 2 = 0
2 + -15n + 7n2 = 0 + n2 + -1n2
2 + -15n + 7n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
2 + -15n + 7n2 = 0

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

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

Simplifying
1 + -7n = 0

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

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

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

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.1428571429, 2}