(2w-9)(w+7)=0

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Solution for (2w-9)(w+7)=0 equation:


Simplifying
(2w + -9)(w + 7) = 0

Reorder the terms:
(-9 + 2w)(w + 7) = 0

Reorder the terms:
(-9 + 2w)(7 + w) = 0

Multiply (-9 + 2w) * (7 + w)
(-9(7 + w) + 2w * (7 + w)) = 0
((7 * -9 + w * -9) + 2w * (7 + w)) = 0
((-63 + -9w) + 2w * (7 + w)) = 0
(-63 + -9w + (7 * 2w + w * 2w)) = 0
(-63 + -9w + (14w + 2w2)) = 0

Combine like terms: -9w + 14w = 5w
(-63 + 5w + 2w2) = 0

Solving
-63 + 5w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(9 + -2w) = 0

Subproblem 1

Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 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 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7

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 = {-7, 4.5}

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