5(X+1)=X^2-1

Solution for 5(X+1)=X^2-1 equation:

Simplifying
5(X + 1) = X2 + -1

Reorder the terms:
5(1 + X) = X2 + -1
(1 * 5 + X * 5) = X2 + -1
(5 + 5X) = X2 + -1

Reorder the terms:
5 + 5X = -1 + X2

Solving
5 + 5X = -1 + X2

Solving for variable 'X'.

Reorder the terms:
5 + 1 + 5X + -1X2 = -1 + X2 + 1 + -1X2

Combine like terms: 5 + 1 = 6
6 + 5X + -1X2 = -1 + X2 + 1 + -1X2

Reorder the terms:
6 + 5X + -1X2 = -1 + 1 + X2 + -1X2

Combine like terms: -1 + 1 = 0
6 + 5X + -1X2 = 0 + X2 + -1X2
6 + 5X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
6 + 5X + -1X2 = 0

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

Subproblem 1
Set the factor '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1X = 0 + -6

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

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

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

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

Simplifying
1 + X = 0

Solving
1 + X = 0

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

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

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

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

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