(w-6)(w-6)=2w^2-10w+28

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Solution for (w-6)(w-6)=2w^2-10w+28 equation: 


Simplifying
(w + -6)(w + -6) = 2w2 + -10w + 28

Reorder the terms:
(-6 + w)(w + -6) = 2w2 + -10w + 28

Reorder the terms:
(-6 + w)(-6 + w) = 2w2 + -10w + 28

Multiply (-6 + w) * (-6 + w)
(-6(-6 + w) + w(-6 + w)) = 2w2 + -10w + 28
((-6 * -6 + w * -6) + w(-6 + w)) = 2w2 + -10w + 28
((36 + -6w) + w(-6 + w)) = 2w2 + -10w + 28
(36 + -6w + (-6 * w + w * w)) = 2w2 + -10w + 28
(36 + -6w + (-6w + w2)) = 2w2 + -10w + 28

Combine like terms: -6w + -6w = -12w
(36 + -12w + w2) = 2w2 + -10w + 28

Reorder the terms:
36 + -12w + w2 = 28 + -10w + 2w2

Solving
36 + -12w + w2 = 28 + -10w + 2w2

Solving for variable 'w'.

Reorder the terms:
36 + -28 + -12w + 10w + w2 + -2w2 = 28 + -10w + 2w2 + -28 + 10w + -2w2

Combine like terms: 36 + -28 = 8
8 + -12w + 10w + w2 + -2w2 = 28 + -10w + 2w2 + -28 + 10w + -2w2

Combine like terms: -12w + 10w = -2w
8 + -2w + w2 + -2w2 = 28 + -10w + 2w2 + -28 + 10w + -2w2

Combine like terms: w2 + -2w2 = -1w2
8 + -2w + -1w2 = 28 + -10w + 2w2 + -28 + 10w + -2w2

Reorder the terms:
8 + -2w + -1w2 = 28 + -28 + -10w + 10w + 2w2 + -2w2

Combine like terms: 28 + -28 = 0
8 + -2w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2
8 + -2w + -1w2 = -10w + 10w + 2w2 + -2w2

Combine like terms: -10w + 10w = 0
8 + -2w + -1w2 = 0 + 2w2 + -2w2
8 + -2w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
8 + -2w + -1w2 = 0

Factor a trinomial.
(2 + -1w)(4 + w) = 0


Subproblem 1
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

Subproblem 2
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
Solution
w = {2, -4}

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