2w^2-2w+21=(w-4)(w-4)

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Solution for 2w^2-2w+21=(w-4)(w-4) equation: 


Simplifying
2w2 + -2w + 21 = (w + -4)(w + -4)

Reorder the terms:
21 + -2w + 2w2 = (w + -4)(w + -4)

Reorder the terms:
21 + -2w + 2w2 = (-4 + w)(w + -4)

Reorder the terms:
21 + -2w + 2w2 = (-4 + w)(-4 + w)

Multiply (-4 + w) * (-4 + w)
21 + -2w + 2w2 = (-4(-4 + w) + w(-4 + w))
21 + -2w + 2w2 = ((-4 * -4 + w * -4) + w(-4 + w))
21 + -2w + 2w2 = ((16 + -4w) + w(-4 + w))
21 + -2w + 2w2 = (16 + -4w + (-4 * w + w * w))
21 + -2w + 2w2 = (16 + -4w + (-4w + w2))

Combine like terms: -4w + -4w = -8w
21 + -2w + 2w2 = (16 + -8w + w2)

Solving
21 + -2w + 2w2 = 16 + -8w + w2

Solving for variable 'w'.

Reorder the terms:
21 + -16 + -2w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 21 + -16 = 5
5 + -2w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: -2w + 8w = 6w
5 + 6w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
5 + 6w + 1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Reorder the terms:
5 + 6w + 1w2 = 16 + -16 + -8w + 8w + w2 + -1w2

Combine like terms: 16 + -16 = 0
5 + 6w + 1w2 = 0 + -8w + 8w + w2 + -1w2
5 + 6w + 1w2 = -8w + 8w + w2 + -1w2

Combine like terms: -8w + 8w = 0
5 + 6w + 1w2 = 0 + w2 + -1w2
5 + 6w + 1w2 = w2 + -1w2

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

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


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

Simplifying
5 + w = 0

Solving
5 + w = 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 + w = 0 + -5

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

Combine like terms: 0 + -5 = -5
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}

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