(2w-9)(3-w)=0

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Solution for (2w-9)(3-w)=0 equation:


Simplifying
(2w + -9)(3 + -1w) = 0

Reorder the terms:
(-9 + 2w)(3 + -1w) = 0

Multiply (-9 + 2w) * (3 + -1w)
(-9(3 + -1w) + 2w * (3 + -1w)) = 0
((3 * -9 + -1w * -9) + 2w * (3 + -1w)) = 0
((-27 + 9w) + 2w * (3 + -1w)) = 0
(-27 + 9w + (3 * 2w + -1w * 2w)) = 0
(-27 + 9w + (6w + -2w2)) = 0

Combine like terms: 9w + 6w = 15w
(-27 + 15w + -2w2) = 0

Solving
-27 + 15w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + 2w)(3 + -1w) = 0

Subproblem 1

Set the factor '(-9 + 2w)' equal to zero and attempt to solve: Simplifying -9 + 2w = 0 Solving -9 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2w = 0 + 9 2w = 0 + 9 Combine like terms: 0 + 9 = 9 2w = 9 Divide each side by '2'. w = 4.5 Simplifying w = 4.5

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 = {4.5, 3}

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