(w*w)+7w+6=0

Solution for (w*w)+7w+6=0 equation:

Simplifying
(w * w) + 7w + 6 = 0

Multiply w * w
(w2) + 7w + 6 = 0
w2 + 7w + 6 = 0

Reorder the terms:
6 + 7w + w2 = 0

Solving
6 + 7w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(1 + w) = 0

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

Simplifying
6 + w = 0

Solving
6 + w = 0

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

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

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

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

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

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