2w^2-7w+22=(w-6)(w-6)

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Solution for 2w^2-7w+22=(w-6)(w-6) equation: 


Simplifying
2w2 + -7w + 22 = (w + -6)(w + -6)

Reorder the terms:
22 + -7w + 2w2 = (w + -6)(w + -6)

Reorder the terms:
22 + -7w + 2w2 = (-6 + w)(w + -6)

Reorder the terms:
22 + -7w + 2w2 = (-6 + w)(-6 + w)

Multiply (-6 + w) * (-6 + w)
22 + -7w + 2w2 = (-6(-6 + w) + w(-6 + w))
22 + -7w + 2w2 = ((-6 * -6 + w * -6) + w(-6 + w))
22 + -7w + 2w2 = ((36 + -6w) + w(-6 + w))
22 + -7w + 2w2 = (36 + -6w + (-6 * w + w * w))
22 + -7w + 2w2 = (36 + -6w + (-6w + w2))

Combine like terms: -6w + -6w = -12w
22 + -7w + 2w2 = (36 + -12w + w2)

Solving
22 + -7w + 2w2 = 36 + -12w + w2

Solving for variable 'w'.

Reorder the terms:
22 + -36 + -7w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: 22 + -36 = -14
-14 + -7w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: -7w + 12w = 5w
-14 + 5w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-14 + 5w + 1w2 = 36 + -12w + w2 + -36 + 12w + -1w2

Reorder the terms:
-14 + 5w + 1w2 = 36 + -36 + -12w + 12w + w2 + -1w2

Combine like terms: 36 + -36 = 0
-14 + 5w + 1w2 = 0 + -12w + 12w + w2 + -1w2
-14 + 5w + 1w2 = -12w + 12w + w2 + -1w2

Combine like terms: -12w + 12w = 0
-14 + 5w + 1w2 = 0 + w2 + -1w2
-14 + 5w + 1w2 = w2 + -1w2

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

Factor a trinomial.
(-7 + -1w)(2 + -1w) = 0


Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-7, 2}

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