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

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


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

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

Multiply (-2 + 4w) * (3 + w)
(-2(3 + w) + 4w * (3 + w)) = 0
((3 * -2 + w * -2) + 4w * (3 + w)) = 0
((-6 + -2w) + 4w * (3 + w)) = 0
(-6 + -2w + (3 * 4w + w * 4w)) = 0
(-6 + -2w + (12w + 4w2)) = 0

Combine like terms: -2w + 12w = 10w
(-6 + 10w + 4w2) = 0

Solving
-6 + 10w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5w + 2w2) = 0

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

Ignore the factor 2.

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 '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5

Solution

w = {-3, 0.5}

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