3(w+7)(-w-6)=0

Solution for 3(w+7)(-w-6)=0 equation:

Simplifying
3(w + 7)(-1w + -6) = 0

Reorder the terms:
3(7 + w)(-1w + -6) = 0

Reorder the terms:
3(7 + w)(-6 + -1w) = 0

Multiply (7 + w) * (-6 + -1w)
3(7(-6 + -1w) + w(-6 + -1w)) = 0
3((-6 * 7 + -1w * 7) + w(-6 + -1w)) = 0
3((-42 + -7w) + w(-6 + -1w)) = 0
3(-42 + -7w + (-6 * w + -1w * w)) = 0
3(-42 + -7w + (-6w + -1w2)) = 0

Combine like terms: -7w + -6w = -13w
3(-42 + -13w + -1w2) = 0
(-42 * 3 + -13w * 3 + -1w2 * 3) = 0
(-126 + -39w + -3w2) = 0

Solving
-126 + -39w + -3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(42 + 13w + w2) = 0

Factor a trinomial.
-3((7 + w)(6 + w)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

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

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Subproblem 2
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
Solution
w = {-7, -6}