(w+2)(w-4)+(w-2)(w+2)=(w-2)(w-3)

Solution for (w+2)(w-4)+(w-2)(w+2)=(w-2)(w-3) equation:

Simplifying
(w + 2)(w + -4) + (w + -2)(w + 2) = (w + -2)(w + -3)

Reorder the terms:
(2 + w)(w + -4) + (w + -2)(w + 2) = (w + -2)(w + -3)

Reorder the terms:
(2 + w)(-4 + w) + (w + -2)(w + 2) = (w + -2)(w + -3)

Multiply (2 + w) * (-4 + w)
(2(-4 + w) + w(-4 + w)) + (w + -2)(w + 2) = (w + -2)(w + -3)
((-4 * 2 + w * 2) + w(-4 + w)) + (w + -2)(w + 2) = (w + -2)(w + -3)
((-8 + 2w) + w(-4 + w)) + (w + -2)(w + 2) = (w + -2)(w + -3)
(-8 + 2w + (-4 * w + w * w)) + (w + -2)(w + 2) = (w + -2)(w + -3)
(-8 + 2w + (-4w + w2)) + (w + -2)(w + 2) = (w + -2)(w + -3)

Combine like terms: 2w + -4w = -2w
(-8 + -2w + w2) + (w + -2)(w + 2) = (w + -2)(w + -3)

Reorder the terms:
-8 + -2w + w2 + (-2 + w)(w + 2) = (w + -2)(w + -3)

Reorder the terms:
-8 + -2w + w2 + (-2 + w)(2 + w) = (w + -2)(w + -3)

Multiply (-2 + w) * (2 + w)
-8 + -2w + w2 + (-2(2 + w) + w(2 + w)) = (w + -2)(w + -3)
-8 + -2w + w2 + ((2 * -2 + w * -2) + w(2 + w)) = (w + -2)(w + -3)
-8 + -2w + w2 + ((-4 + -2w) + w(2 + w)) = (w + -2)(w + -3)
-8 + -2w + w2 + (-4 + -2w + (2 * w + w * w)) = (w + -2)(w + -3)
-8 + -2w + w2 + (-4 + -2w + (2w + w2)) = (w + -2)(w + -3)

Combine like terms: -2w + 2w = 0
-8 + -2w + w2 + (-4 + 0 + w2) = (w + -2)(w + -3)
-8 + -2w + w2 + (-4 + w2) = (w + -2)(w + -3)

Reorder the terms:
-8 + -4 + -2w + w2 + w2 = (w + -2)(w + -3)

Combine like terms: -8 + -4 = -12
-12 + -2w + w2 + w2 = (w + -2)(w + -3)

Combine like terms: w2 + w2 = 2w2
-12 + -2w + 2w2 = (w + -2)(w + -3)

Reorder the terms:
-12 + -2w + 2w2 = (-2 + w)(w + -3)

Reorder the terms:
-12 + -2w + 2w2 = (-2 + w)(-3 + w)

Multiply (-2 + w) * (-3 + w)
-12 + -2w + 2w2 = (-2(-3 + w) + w(-3 + w))
-12 + -2w + 2w2 = ((-3 * -2 + w * -2) + w(-3 + w))
-12 + -2w + 2w2 = ((6 + -2w) + w(-3 + w))
-12 + -2w + 2w2 = (6 + -2w + (-3 * w + w * w))
-12 + -2w + 2w2 = (6 + -2w + (-3w + w2))

Combine like terms: -2w + -3w = -5w
-12 + -2w + 2w2 = (6 + -5w + w2)

Solving
-12 + -2w + 2w2 = 6 + -5w + w2

Solving for variable 'w'.

Reorder the terms:
-12 + -6 + -2w + 5w + 2w2 + -1w2 = 6 + -5w + w2 + -6 + 5w + -1w2

Combine like terms: -12 + -6 = -18
-18 + -2w + 5w + 2w2 + -1w2 = 6 + -5w + w2 + -6 + 5w + -1w2

Combine like terms: -2w + 5w = 3w
-18 + 3w + 2w2 + -1w2 = 6 + -5w + w2 + -6 + 5w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-18 + 3w + 1w2 = 6 + -5w + w2 + -6 + 5w + -1w2

Reorder the terms:
-18 + 3w + 1w2 = 6 + -6 + -5w + 5w + w2 + -1w2

Combine like terms: 6 + -6 = 0
-18 + 3w + 1w2 = 0 + -5w + 5w + w2 + -1w2
-18 + 3w + 1w2 = -5w + 5w + w2 + -1w2

Combine like terms: -5w + 5w = 0
-18 + 3w + 1w2 = 0 + w2 + -1w2
-18 + 3w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-18 + 3w + 1w2 = 0

Factor a trinomial.
(-6 + -1w)(3 + -1w) = 0

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

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 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 + -1w = 0 + 6

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

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

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-6, 3}