2w^2+2w-4=(w-1)(w-1)

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Solution for 2w^2+2w-4=(w-1)(w-1) equation: 


Simplifying
2w2 + 2w + -4 = (w + -1)(w + -1)

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

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

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

Multiply (-1 + w) * (-1 + w)
-4 + 2w + 2w2 = (-1(-1 + w) + w(-1 + w))
-4 + 2w + 2w2 = ((-1 * -1 + w * -1) + w(-1 + w))
-4 + 2w + 2w2 = ((1 + -1w) + w(-1 + w))
-4 + 2w + 2w2 = (1 + -1w + (-1 * w + w * w))
-4 + 2w + 2w2 = (1 + -1w + (-1w + w2))

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

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

Solving for variable 'w'.

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

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

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

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

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

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

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

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

Factor a trinomial.
(-5 + -1w)(1 + -1w) = 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 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-5, 1}

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