(w+1)(w+1)=2(w-2)(w+1)

Solution for (w+1)(w+1)=2(w-2)(w+1) equation:

Simplifying
(w + 1)(w + 1) = 2(w + -2)(w + 1)

Reorder the terms:
(1 + w)(w + 1) = 2(w + -2)(w + 1)

Reorder the terms:
(1 + w)(1 + w) = 2(w + -2)(w + 1)

Multiply (1 + w) * (1 + w)
(1(1 + w) + w(1 + w)) = 2(w + -2)(w + 1)
((1 * 1 + w * 1) + w(1 + w)) = 2(w + -2)(w + 1)
((1 + 1w) + w(1 + w)) = 2(w + -2)(w + 1)
(1 + 1w + (1 * w + w * w)) = 2(w + -2)(w + 1)
(1 + 1w + (1w + w2)) = 2(w + -2)(w + 1)

Combine like terms: 1w + 1w = 2w
(1 + 2w + w2) = 2(w + -2)(w + 1)

Reorder the terms:
1 + 2w + w2 = 2(-2 + w)(w + 1)

Reorder the terms:
1 + 2w + w2 = 2(-2 + w)(1 + w)

Multiply (-2 + w) * (1 + w)
1 + 2w + w2 = 2(-2(1 + w) + w(1 + w))
1 + 2w + w2 = 2((1 * -2 + w * -2) + w(1 + w))
1 + 2w + w2 = 2((-2 + -2w) + w(1 + w))
1 + 2w + w2 = 2(-2 + -2w + (1 * w + w * w))
1 + 2w + w2 = 2(-2 + -2w + (1w + w2))

Combine like terms: -2w + 1w = -1w
1 + 2w + w2 = 2(-2 + -1w + w2)
1 + 2w + w2 = (-2 * 2 + -1w * 2 + w2 * 2)
1 + 2w + w2 = (-4 + -2w + 2w2)

Solving
1 + 2w + w2 = -4 + -2w + 2w2

Solving for variable 'w'.

Reorder the terms:
1 + 4 + 2w + 2w + w2 + -2w2 = -4 + -2w + 2w2 + 4 + 2w + -2w2

Combine like terms: 1 + 4 = 5
5 + 2w + 2w + w2 + -2w2 = -4 + -2w + 2w2 + 4 + 2w + -2w2

Combine like terms: 2w + 2w = 4w
5 + 4w + w2 + -2w2 = -4 + -2w + 2w2 + 4 + 2w + -2w2

Combine like terms: w2 + -2w2 = -1w2
5 + 4w + -1w2 = -4 + -2w + 2w2 + 4 + 2w + -2w2

Reorder the terms:
5 + 4w + -1w2 = -4 + 4 + -2w + 2w + 2w2 + -2w2

Combine like terms: -4 + 4 = 0
5 + 4w + -1w2 = 0 + -2w + 2w + 2w2 + -2w2
5 + 4w + -1w2 = -2w + 2w + 2w2 + -2w2

Combine like terms: -2w + 2w = 0
5 + 4w + -1w2 = 0 + 2w2 + -2w2
5 + 4w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
5 + 4w + -1w2 = 0

Factor a trinomial.
(5 + -1w)(1 + w) = 0

Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
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 = {5, -1}