w^2-1=w+5

Solution for w^2-1=w+5 equation:

Simplifying
w2 + -1 = w + 5

Reorder the terms:
-1 + w2 = w + 5

Reorder the terms:
-1 + w2 = 5 + w

Solving
-1 + w2 = 5 + w

Solving for variable 'w'.

Reorder the terms:
-1 + -5 + -1w + w2 = 5 + w + -5 + -1w

Combine like terms: -1 + -5 = -6
-6 + -1w + w2 = 5 + w + -5 + -1w

Reorder the terms:
-6 + -1w + w2 = 5 + -5 + w + -1w

Combine like terms: 5 + -5 = 0
-6 + -1w + w2 = 0 + w + -1w
-6 + -1w + w2 = w + -1w

Combine like terms: w + -1w = 0
-6 + -1w + w2 = 0

Factor a trinomial.
(-2 + -1w)(3 + -1w) = 0

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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

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

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

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

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

Simplifying
w = -2
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-2, 3}