(w-5)(w-5)=2w^2-12w+10

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Solution for (w-5)(w-5)=2w^2-12w+10 equation: 


Simplifying
(w + -5)(w + -5) = 2w2 + -12w + 10

Reorder the terms:
(-5 + w)(w + -5) = 2w2 + -12w + 10

Reorder the terms:
(-5 + w)(-5 + w) = 2w2 + -12w + 10

Multiply (-5 + w) * (-5 + w)
(-5(-5 + w) + w(-5 + w)) = 2w2 + -12w + 10
((-5 * -5 + w * -5) + w(-5 + w)) = 2w2 + -12w + 10
((25 + -5w) + w(-5 + w)) = 2w2 + -12w + 10
(25 + -5w + (-5 * w + w * w)) = 2w2 + -12w + 10
(25 + -5w + (-5w + w2)) = 2w2 + -12w + 10

Combine like terms: -5w + -5w = -10w
(25 + -10w + w2) = 2w2 + -12w + 10

Reorder the terms:
25 + -10w + w2 = 10 + -12w + 2w2

Solving
25 + -10w + w2 = 10 + -12w + 2w2

Solving for variable 'w'.

Reorder the terms:
25 + -10 + -10w + 12w + w2 + -2w2 = 10 + -12w + 2w2 + -10 + 12w + -2w2

Combine like terms: 25 + -10 = 15
15 + -10w + 12w + w2 + -2w2 = 10 + -12w + 2w2 + -10 + 12w + -2w2

Combine like terms: -10w + 12w = 2w
15 + 2w + w2 + -2w2 = 10 + -12w + 2w2 + -10 + 12w + -2w2

Combine like terms: w2 + -2w2 = -1w2
15 + 2w + -1w2 = 10 + -12w + 2w2 + -10 + 12w + -2w2

Reorder the terms:
15 + 2w + -1w2 = 10 + -10 + -12w + 12w + 2w2 + -2w2

Combine like terms: 10 + -10 = 0
15 + 2w + -1w2 = 0 + -12w + 12w + 2w2 + -2w2
15 + 2w + -1w2 = -12w + 12w + 2w2 + -2w2

Combine like terms: -12w + 12w = 0
15 + 2w + -1w2 = 0 + 2w2 + -2w2
15 + 2w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
15 + 2w + -1w2 = 0

Factor a trinomial.
(5 + -1w)(3 + w) = 0


Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5

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

Simplifying
3 + w = 0

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

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

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

Simplifying
w = -3
Solution
w = {5, -3}

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