(6+w)(2w-9)=0

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Solution for (6+w)(2w-9)=0 equation:


Simplifying
(6 + w)(2w + -9) = 0

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

Multiply (6 + w) * (-9 + 2w)
(6(-9 + 2w) + w(-9 + 2w)) = 0
((-9 * 6 + 2w * 6) + w(-9 + 2w)) = 0
((-54 + 12w) + w(-9 + 2w)) = 0
(-54 + 12w + (-9 * w + 2w * w)) = 0
(-54 + 12w + (-9w + 2w2)) = 0

Combine like terms: 12w + -9w = 3w
(-54 + 3w + 2w2) = 0

Solving
-54 + 3w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(9 + -2w) = 0

Subproblem 1

Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6

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 = {-6, 4.5}

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