(8-w)(4w-2)=0

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Solution for (8-w)(4w-2)=0 equation: 


Simplifying
(8 + -1w)(4w + -2) = 0

Reorder the terms:
(8 + -1w)(-2 + 4w) = 0

Multiply (8 + -1w) * (-2 + 4w)
(8(-2 + 4w) + -1w * (-2 + 4w)) = 0
((-2 * 8 + 4w * 8) + -1w * (-2 + 4w)) = 0
((-16 + 32w) + -1w * (-2 + 4w)) = 0
(-16 + 32w + (-2 * -1w + 4w * -1w)) = 0
(-16 + 32w + (2w + -4w2)) = 0

Combine like terms: 32w + 2w = 34w
(-16 + 34w + -4w2) = 0

Solving
-16 + 34w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 17w + -2w2) = 0

Factor a trinomial.
2((-8 + w)(1 + -2w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + w)' equal to zero and attempt to solve:

Simplifying
-8 + w = 0

Solving
-8 + w = 0

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

Add '8' to each side of the equation.
-8 + 8 + w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + w = 0 + 8
w = 0 + 8

Combine like terms: 0 + 8 = 8
w = 8

Simplifying
w = 8

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

Simplifying
1 + -2w = 0

Solving
1 + -2w = 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 + -2w = 0 + -1

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

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

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {8, 0.5}

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