2w^2-6w+8=(w-4)(w-4)

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Solution for 2w^2-6w+8=(w-4)(w-4) equation: 


Simplifying
2w2 + -6w + 8 = (w + -4)(w + -4)

Reorder the terms:
8 + -6w + 2w2 = (w + -4)(w + -4)

Reorder the terms:
8 + -6w + 2w2 = (-4 + w)(w + -4)

Reorder the terms:
8 + -6w + 2w2 = (-4 + w)(-4 + w)

Multiply (-4 + w) * (-4 + w)
8 + -6w + 2w2 = (-4(-4 + w) + w(-4 + w))
8 + -6w + 2w2 = ((-4 * -4 + w * -4) + w(-4 + w))
8 + -6w + 2w2 = ((16 + -4w) + w(-4 + w))
8 + -6w + 2w2 = (16 + -4w + (-4 * w + w * w))
8 + -6w + 2w2 = (16 + -4w + (-4w + w2))

Combine like terms: -4w + -4w = -8w
8 + -6w + 2w2 = (16 + -8w + w2)

Solving
8 + -6w + 2w2 = 16 + -8w + w2

Solving for variable 'w'.

Reorder the terms:
8 + -16 + -6w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 8 + -16 = -8
-8 + -6w + 8w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: -6w + 8w = 2w
-8 + 2w + 2w2 + -1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-8 + 2w + 1w2 = 16 + -8w + w2 + -16 + 8w + -1w2

Reorder the terms:
-8 + 2w + 1w2 = 16 + -16 + -8w + 8w + w2 + -1w2

Combine like terms: 16 + -16 = 0
-8 + 2w + 1w2 = 0 + -8w + 8w + w2 + -1w2
-8 + 2w + 1w2 = -8w + 8w + w2 + -1w2

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

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

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


Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 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 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
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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