(3+w)(3w-4)=0

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Solution for (3+w)(3w-4)=0 equation:


Simplifying
(3 + w)(3w + -4) = 0

Reorder the terms:
(3 + w)(-4 + 3w) = 0

Multiply (3 + w) * (-4 + 3w)
(3(-4 + 3w) + w(-4 + 3w)) = 0
((-4 * 3 + 3w * 3) + w(-4 + 3w)) = 0
((-12 + 9w) + w(-4 + 3w)) = 0
(-12 + 9w + (-4 * w + 3w * w)) = 0
(-12 + 9w + (-4w + 3w2)) = 0

Combine like terms: 9w + -4w = 5w
(-12 + 5w + 3w2) = 0

Solving
-12 + 5w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(4 + -3w) = 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 '(4 + -3w)' equal to zero and attempt to solve: Simplifying 4 + -3w = 0 Solving 4 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3w = 0 + -4 -3w = 0 + -4 Combine like terms: 0 + -4 = -4 -3w = -4 Divide each side by '-3'. w = 1.333333333 Simplifying w = 1.333333333

Solution

w = {-3, 1.333333333}

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