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

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


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

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

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

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

Solving
2 + 5w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + -1w)(1 + 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 '(1 + 3w)' equal to zero and attempt to solve: Simplifying 1 + 3w = 0 Solving 1 + 3w = 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 + 3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3w = 0 + -1 3w = 0 + -1 Combine like terms: 0 + -1 = -1 3w = -1 Divide each side by '3'. w = -0.3333333333 Simplifying w = -0.3333333333

Solution

w = {2, -0.3333333333}

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