(w-2)(w-2)=2w^2-10w+12

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Solution for (w-2)(w-2)=2w^2-10w+12 equation: 


Simplifying
(w + -2)(w + -2) = 2w2 + -10w + 12

Reorder the terms:
(-2 + w)(w + -2) = 2w2 + -10w + 12

Reorder the terms:
(-2 + w)(-2 + w) = 2w2 + -10w + 12

Multiply (-2 + w) * (-2 + w)
(-2(-2 + w) + w(-2 + w)) = 2w2 + -10w + 12
((-2 * -2 + w * -2) + w(-2 + w)) = 2w2 + -10w + 12
((4 + -2w) + w(-2 + w)) = 2w2 + -10w + 12
(4 + -2w + (-2 * w + w * w)) = 2w2 + -10w + 12
(4 + -2w + (-2w + w2)) = 2w2 + -10w + 12

Combine like terms: -2w + -2w = -4w
(4 + -4w + w2) = 2w2 + -10w + 12

Reorder the terms:
4 + -4w + w2 = 12 + -10w + 2w2

Solving
4 + -4w + w2 = 12 + -10w + 2w2

Solving for variable 'w'.

Reorder the terms:
4 + -12 + -4w + 10w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2

Combine like terms: 4 + -12 = -8
-8 + -4w + 10w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2

Combine like terms: -4w + 10w = 6w
-8 + 6w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-8 + 6w + -1w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2

Reorder the terms:
-8 + 6w + -1w2 = 12 + -12 + -10w + 10w + 2w2 + -2w2

Combine like terms: 12 + -12 = 0
-8 + 6w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2
-8 + 6w + -1w2 = -10w + 10w + 2w2 + -2w2

Combine like terms: -10w + 10w = 0
-8 + 6w + -1w2 = 0 + 2w2 + -2w2
-8 + 6w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-8 + 6w + -1w2 = 0

Factor a trinomial.
(-4 + w)(2 + -1w) = 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 '(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 = {4, 2}

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