w(w+1)-5(w+1)=

Solution for w(w+1)-5(w+1)= equation:

Simplifying
w(w + 1) + -5(w + 1) = 0

Reorder the terms:
w(1 + w) + -5(w + 1) = 0
(1 * w + w * w) + -5(w + 1) = 0
(1w + w2) + -5(w + 1) = 0

Reorder the terms:
1w + w2 + -5(1 + w) = 0
1w + w2 + (1 * -5 + w * -5) = 0
1w + w2 + (-5 + -5w) = 0

Reorder the terms:
-5 + 1w + -5w + w2 = 0

Combine like terms: 1w + -5w = -4w
-5 + -4w + w2 = 0

Solving
-5 + -4w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(5 + -1w) = 0

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

Simplifying
w = -1
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-1, 5}