(w-1)(w-1)=2w^2-10w+8

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Solution for (w-1)(w-1)=2w^2-10w+8 equation: 


Simplifying
(w + -1)(w + -1) = 2w2 + -10w + 8

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

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

Multiply (-1 + w) * (-1 + w)
(-1(-1 + w) + w(-1 + w)) = 2w2 + -10w + 8
((-1 * -1 + w * -1) + w(-1 + w)) = 2w2 + -10w + 8
((1 + -1w) + w(-1 + w)) = 2w2 + -10w + 8
(1 + -1w + (-1 * w + w * w)) = 2w2 + -10w + 8
(1 + -1w + (-1w + w2)) = 2w2 + -10w + 8

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

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

Solving
1 + -2w + w2 = 8 + -10w + 2w2

Solving for variable 'w'.

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

Combine like terms: 1 + -8 = -7
-7 + -2w + 10w + w2 + -2w2 = 8 + -10w + 2w2 + -8 + 10w + -2w2

Combine like terms: -2w + 10w = 8w
-7 + 8w + w2 + -2w2 = 8 + -10w + 2w2 + -8 + 10w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-7 + 8w + -1w2 = 8 + -10w + 2w2 + -8 + 10w + -2w2

Reorder the terms:
-7 + 8w + -1w2 = 8 + -8 + -10w + 10w + 2w2 + -2w2

Combine like terms: 8 + -8 = 0
-7 + 8w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2
-7 + 8w + -1w2 = -10w + 10w + 2w2 + -2w2

Combine like terms: -10w + 10w = 0
-7 + 8w + -1w2 = 0 + 2w2 + -2w2
-7 + 8w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-7 + 8w + -1w2 = 0

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


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

Simplifying
-7 + w = 0

Solving
-7 + w = 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 + w = 0 + 7

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

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

Simplifying
w = 7

Subproblem 2
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
Solution
w = {7, 1}

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