(2w+1)(3-w)=0

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Solution for (2w+1)(3-w)=0 equation:


Simplifying
(2w + 1)(3 + -1w) = 0

Reorder the terms:
(1 + 2w)(3 + -1w) = 0

Multiply (1 + 2w) * (3 + -1w)
(1(3 + -1w) + 2w * (3 + -1w)) = 0
((3 * 1 + -1w * 1) + 2w * (3 + -1w)) = 0
((3 + -1w) + 2w * (3 + -1w)) = 0
(3 + -1w + (3 * 2w + -1w * 2w)) = 0
(3 + -1w + (6w + -2w2)) = 0

Combine like terms: -1w + 6w = 5w
(3 + 5w + -2w2) = 0

Solving
3 + 5w + -2w2 = 0

Solving for variable 'w'.

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