(w-5)(w-5)=2w^2-6w+28

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Solution for (w-5)(w-5)=2w^2-6w+28 equation: 


Simplifying
(w + -5)(w + -5) = 2w2 + -6w + 28

Reorder the terms:
(-5 + w)(w + -5) = 2w2 + -6w + 28

Reorder the terms:
(-5 + w)(-5 + w) = 2w2 + -6w + 28

Multiply (-5 + w) * (-5 + w)
(-5(-5 + w) + w(-5 + w)) = 2w2 + -6w + 28
((-5 * -5 + w * -5) + w(-5 + w)) = 2w2 + -6w + 28
((25 + -5w) + w(-5 + w)) = 2w2 + -6w + 28
(25 + -5w + (-5 * w + w * w)) = 2w2 + -6w + 28
(25 + -5w + (-5w + w2)) = 2w2 + -6w + 28

Combine like terms: -5w + -5w = -10w
(25 + -10w + w2) = 2w2 + -6w + 28

Reorder the terms:
25 + -10w + w2 = 28 + -6w + 2w2

Solving
25 + -10w + w2 = 28 + -6w + 2w2

Solving for variable 'w'.

Reorder the terms:
25 + -28 + -10w + 6w + w2 + -2w2 = 28 + -6w + 2w2 + -28 + 6w + -2w2

Combine like terms: 25 + -28 = -3
-3 + -10w + 6w + w2 + -2w2 = 28 + -6w + 2w2 + -28 + 6w + -2w2

Combine like terms: -10w + 6w = -4w
-3 + -4w + w2 + -2w2 = 28 + -6w + 2w2 + -28 + 6w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-3 + -4w + -1w2 = 28 + -6w + 2w2 + -28 + 6w + -2w2

Reorder the terms:
-3 + -4w + -1w2 = 28 + -28 + -6w + 6w + 2w2 + -2w2

Combine like terms: 28 + -28 = 0
-3 + -4w + -1w2 = 0 + -6w + 6w + 2w2 + -2w2
-3 + -4w + -1w2 = -6w + 6w + 2w2 + -2w2

Combine like terms: -6w + 6w = 0
-3 + -4w + -1w2 = 0 + 2w2 + -2w2
-3 + -4w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-3 + -4w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4w + w2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {-3, -1}

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