5n^2-5n-7=4n^2-1

Solution for 5n^2-5n-7=4n^2-1 equation:

Simplifying
5n2 + -5n + -7 = 4n2 + -1

Reorder the terms:
-7 + -5n + 5n2 = 4n2 + -1

Reorder the terms:
-7 + -5n + 5n2 = -1 + 4n2

Solving
-7 + -5n + 5n2 = -1 + 4n2

Solving for variable 'n'.

Reorder the terms:
-7 + 1 + -5n + 5n2 + -4n2 = -1 + 4n2 + 1 + -4n2

Combine like terms: -7 + 1 = -6
-6 + -5n + 5n2 + -4n2 = -1 + 4n2 + 1 + -4n2

Combine like terms: 5n2 + -4n2 = 1n2
-6 + -5n + 1n2 = -1 + 4n2 + 1 + -4n2

Reorder the terms:
-6 + -5n + 1n2 = -1 + 1 + 4n2 + -4n2

Combine like terms: -1 + 1 = 0
-6 + -5n + 1n2 = 0 + 4n2 + -4n2
-6 + -5n + 1n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-6 + -5n + 1n2 = 0

Factor a trinomial.
(-1 + -1n)(6 + -1n) = 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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-1, 6}