2w^2+2w+13=(w-2)(w-2)

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Solution for 2w^2+2w+13=(w-2)(w-2) equation: 


Simplifying
2w2 + 2w + 13 = (w + -2)(w + -2)

Reorder the terms:
13 + 2w + 2w2 = (w + -2)(w + -2)

Reorder the terms:
13 + 2w + 2w2 = (-2 + w)(w + -2)

Reorder the terms:
13 + 2w + 2w2 = (-2 + w)(-2 + w)

Multiply (-2 + w) * (-2 + w)
13 + 2w + 2w2 = (-2(-2 + w) + w(-2 + w))
13 + 2w + 2w2 = ((-2 * -2 + w * -2) + w(-2 + w))
13 + 2w + 2w2 = ((4 + -2w) + w(-2 + w))
13 + 2w + 2w2 = (4 + -2w + (-2 * w + w * w))
13 + 2w + 2w2 = (4 + -2w + (-2w + w2))

Combine like terms: -2w + -2w = -4w
13 + 2w + 2w2 = (4 + -4w + w2)

Solving
13 + 2w + 2w2 = 4 + -4w + w2

Solving for variable 'w'.

Reorder the terms:
13 + -4 + 2w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 13 + -4 = 9
9 + 2w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 2w + 4w = 6w
9 + 6w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
9 + 6w + 1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Reorder the terms:
9 + 6w + 1w2 = 4 + -4 + -4w + 4w + w2 + -1w2

Combine like terms: 4 + -4 = 0
9 + 6w + 1w2 = 0 + -4w + 4w + w2 + -1w2
9 + 6w + 1w2 = -4w + 4w + w2 + -1w2

Combine like terms: -4w + 4w = 0
9 + 6w + 1w2 = 0 + w2 + -1w2
9 + 6w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
9 + 6w + 1w2 = 0

Factor a trinomial.
(3 + w)(3 + w) = 0


Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

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

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

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

Simplifying
w = -3

Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

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

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

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

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

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