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

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Solution for (3-w)(2w-7)=0 equation:


Simplifying
(3 + -1w)(2w + -7) = 0

Reorder the terms:
(3 + -1w)(-7 + 2w) = 0

Multiply (3 + -1w) * (-7 + 2w)
(3(-7 + 2w) + -1w * (-7 + 2w)) = 0
((-7 * 3 + 2w * 3) + -1w * (-7 + 2w)) = 0
((-21 + 6w) + -1w * (-7 + 2w)) = 0
(-21 + 6w + (-7 * -1w + 2w * -1w)) = 0
(-21 + 6w + (7w + -2w2)) = 0

Combine like terms: 6w + 7w = 13w
(-21 + 13w + -2w2) = 0

Solving
-21 + 13w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + 2w)(3 + -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 '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Solution

w = {3.5, 3}

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