-6=w(w+5)

Solution for -6=w(w+5) equation:

Simplifying
-6 = w(w + 5)

Reorder the terms:
-6 = w(5 + w)
-6 = (5 * w + w * w)
-6 = (5w + w2)

Solving
-6 = 5w + w2

Solving for variable 'w'.

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5w + w2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

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

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

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

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

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