(9+w)(4w-6)=0

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Solution for (9+w)(4w-6)=0 equation:


Simplifying
(9 + w)(4w + -6) = 0

Reorder the terms:
(9 + w)(-6 + 4w) = 0

Multiply (9 + w) * (-6 + 4w)
(9(-6 + 4w) + w(-6 + 4w)) = 0
((-6 * 9 + 4w * 9) + w(-6 + 4w)) = 0
((-54 + 36w) + w(-6 + 4w)) = 0
(-54 + 36w + (-6 * w + 4w * w)) = 0
(-54 + 36w + (-6w + 4w2)) = 0

Combine like terms: 36w + -6w = 30w
(-54 + 30w + 4w2) = 0

Solving
-54 + 30w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 15w + 2w2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 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 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9

Subproblem 2

Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5

Solution

w = {-9, 1.5}

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