2w^2-14w+33=(w-6)(w-6)

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Solution for 2w^2-14w+33=(w-6)(w-6) equation: 


Simplifying
2w2 + -14w + 33 = (w + -6)(w + -6)

Reorder the terms:
33 + -14w + 2w2 = (w + -6)(w + -6)

Reorder the terms:
33 + -14w + 2w2 = (-6 + w)(w + -6)

Reorder the terms:
33 + -14w + 2w2 = (-6 + w)(-6 + w)

Multiply (-6 + w) * (-6 + w)
33 + -14w + 2w2 = (-6(-6 + w) + w(-6 + w))
33 + -14w + 2w2 = ((-6 * -6 + w * -6) + w(-6 + w))
33 + -14w + 2w2 = ((36 + -6w) + w(-6 + w))
33 + -14w + 2w2 = (36 + -6w + (-6 * w + w * w))
33 + -14w + 2w2 = (36 + -6w + (-6w + w2))

Combine like terms: -6w + -6w = -12w
33 + -14w + 2w2 = (36 + -12w + w2)

Solving
33 + -14w + 2w2 = 36 + -12w + w2

Solving for variable 'w'.

Reorder the terms:
33 + -36 + -14w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: 33 + -36 = -3
-3 + -14w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: -14w + 12w = -2w
-3 + -2w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-3 + -2w + 1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Reorder the terms:
-3 + -2w + 1w2 = 36 + -36 + -12w + 12w + w2 + -1w2

Combine like terms: 36 + -36 = 0
-3 + -2w + 1w2 = 0 + -12w + 12w + w2 + -1w2
-3 + -2w + 1w2 = -12w + 12w + w2 + -1w2

Combine like terms: -12w + 12w = 0
-3 + -2w + 1w2 = 0 + w2 + -1w2
-3 + -2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-3 + -2w + 1w2 = 0

Factor a trinomial.
(-1 + -1w)(3 + -1w) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-1, 3}

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