(w+1)(w-5)-(w-6)(w-5)-(w+7)(w-6)=0

Solution for (w+1)(w-5)-(w-6)(w-5)-(w+7)(w-6)=0 equation:

Simplifying
(w + 1)(w + -5) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0

Reorder the terms:
(1 + w)(w + -5) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0

Reorder the terms:
(1 + w)(-5 + w) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0

Multiply (1 + w) * (-5 + w)
(1(-5 + w) + w(-5 + w)) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0
((-5 * 1 + w * 1) + w(-5 + w)) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0
((-5 + 1w) + w(-5 + w)) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0
(-5 + 1w + (-5 * w + w * w)) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0
(-5 + 1w + (-5w + w2)) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0

Combine like terms: 1w + -5w = -4w
(-5 + -4w + w2) + -1(w + -6)(w + -5) + -1(w + 7)(w + -6) = 0

Reorder the terms:
-5 + -4w + w2 + -1(-6 + w)(w + -5) + -1(w + 7)(w + -6) = 0

Reorder the terms:
-5 + -4w + w2 + -1(-6 + w)(-5 + w) + -1(w + 7)(w + -6) = 0

Multiply (-6 + w) * (-5 + w)
-5 + -4w + w2 + -1(-6(-5 + w) + w(-5 + w)) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + -1((-5 * -6 + w * -6) + w(-5 + w)) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + -1((30 + -6w) + w(-5 + w)) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + -1(30 + -6w + (-5 * w + w * w)) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + -1(30 + -6w + (-5w + w2)) + -1(w + 7)(w + -6) = 0

Combine like terms: -6w + -5w = -11w
-5 + -4w + w2 + -1(30 + -11w + w2) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + (30 * -1 + -11w * -1 + w2 * -1) + -1(w + 7)(w + -6) = 0
-5 + -4w + w2 + (-30 + 11w + -1w2) + -1(w + 7)(w + -6) = 0

Reorder the terms:
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(7 + w)(w + -6) = 0

Reorder the terms:
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(7 + w)(-6 + w) = 0

Multiply (7 + w) * (-6 + w)
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(7(-6 + w) + w(-6 + w)) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + -1((-6 * 7 + w * 7) + w(-6 + w)) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + -1((-42 + 7w) + w(-6 + w)) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(-42 + 7w + (-6 * w + w * w)) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(-42 + 7w + (-6w + w2)) = 0

Combine like terms: 7w + -6w = 1w
-5 + -4w + w2 + -30 + 11w + -1w2 + -1(-42 + 1w + w2) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + (-42 * -1 + 1w * -1 + w2 * -1) = 0
-5 + -4w + w2 + -30 + 11w + -1w2 + (42 + -1w + -1w2) = 0

Reorder the terms:
-5 + -30 + 42 + -4w + 11w + -1w + w2 + -1w2 + -1w2 = 0

Combine like terms: -5 + -30 = -35
-35 + 42 + -4w + 11w + -1w + w2 + -1w2 + -1w2 = 0

Combine like terms: -35 + 42 = 7
7 + -4w + 11w + -1w + w2 + -1w2 + -1w2 = 0

Combine like terms: -4w + 11w = 7w
7 + 7w + -1w + w2 + -1w2 + -1w2 = 0

Combine like terms: 7w + -1w = 6w
7 + 6w + w2 + -1w2 + -1w2 = 0

Combine like terms: w2 + -1w2 = 0
7 + 6w + 0 + -1w2 = 0
7 + 6w + -1w2 = 0

Solving
7 + 6w + -1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + -1w)(1 + w) = 0

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

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
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 = {7, -1}