(2w-7)(2-w)=0

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Solution for (2w-7)(2-w)=0 equation:


Simplifying
(2w + -7)(2 + -1w) = 0

Reorder the terms:
(-7 + 2w)(2 + -1w) = 0

Multiply (-7 + 2w) * (2 + -1w)
(-7(2 + -1w) + 2w * (2 + -1w)) = 0
((2 * -7 + -1w * -7) + 2w * (2 + -1w)) = 0
((-14 + 7w) + 2w * (2 + -1w)) = 0
(-14 + 7w + (2 * 2w + -1w * 2w)) = 0
(-14 + 7w + (4w + -2w2)) = 0

Combine like terms: 7w + 4w = 11w
(-14 + 11w + -2w2) = 0

Solving
-14 + 11w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + 2w)(2 + -1w) = 0

Subproblem 1

Set the factor '(-7 + 2w)' equal to zero and attempt to solve: Simplifying -7 + 2w = 0 Solving -7 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2w = 0 + 7 2w = 0 + 7 Combine like terms: 0 + 7 = 7 2w = 7 Divide each side by '2'. w = 3.5 Simplifying w = 3.5

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 = {3.5, 2}

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