(3w-4)(2+w)=0

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Solution for (3w-4)(2+w)=0 equation:


Simplifying
(3w + -4)(2 + w) = 0

Reorder the terms:
(-4 + 3w)(2 + w) = 0

Multiply (-4 + 3w) * (2 + w)
(-4(2 + w) + 3w * (2 + w)) = 0
((2 * -4 + w * -4) + 3w * (2 + w)) = 0
((-8 + -4w) + 3w * (2 + w)) = 0
(-8 + -4w + (2 * 3w + w * 3w)) = 0
(-8 + -4w + (6w + 3w2)) = 0

Combine like terms: -4w + 6w = 2w
(-8 + 2w + 3w2) = 0

Solving
-8 + 2w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2 + -1w)(4 + -3w) = 0

Subproblem 1

Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2

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 = {-2, 1.333333333}

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