2w^2-9w+53=(w-7)(w-7)

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Solution for 2w^2-9w+53=(w-7)(w-7) equation: 


Simplifying
2w2 + -9w + 53 = (w + -7)(w + -7)

Reorder the terms:
53 + -9w + 2w2 = (w + -7)(w + -7)

Reorder the terms:
53 + -9w + 2w2 = (-7 + w)(w + -7)

Reorder the terms:
53 + -9w + 2w2 = (-7 + w)(-7 + w)

Multiply (-7 + w) * (-7 + w)
53 + -9w + 2w2 = (-7(-7 + w) + w(-7 + w))
53 + -9w + 2w2 = ((-7 * -7 + w * -7) + w(-7 + w))
53 + -9w + 2w2 = ((49 + -7w) + w(-7 + w))
53 + -9w + 2w2 = (49 + -7w + (-7 * w + w * w))
53 + -9w + 2w2 = (49 + -7w + (-7w + w2))

Combine like terms: -7w + -7w = -14w
53 + -9w + 2w2 = (49 + -14w + w2)

Solving
53 + -9w + 2w2 = 49 + -14w + w2

Solving for variable 'w'.

Reorder the terms:
53 + -49 + -9w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: 53 + -49 = 4
4 + -9w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: -9w + 14w = 5w
4 + 5w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
4 + 5w + 1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Reorder the terms:
4 + 5w + 1w2 = 49 + -49 + -14w + 14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
4 + 5w + 1w2 = 0 + -14w + 14w + w2 + -1w2
4 + 5w + 1w2 = -14w + 14w + w2 + -1w2

Combine like terms: -14w + 14w = 0
4 + 5w + 1w2 = 0 + w2 + -1w2
4 + 5w + 1w2 = w2 + -1w2

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

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


Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4

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 = {-4, -1}

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