(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 = -3w
(27 + -3w + -2w2) = 0

Solving
27 + -3w + -2w2 = 0

Solving for variable 'w'.

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

Subproblem 1

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

Subproblem 2

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

Solution

w = {3, -4.5}

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