(2+w)(5w-1)=0

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Solution for (2+w)(5w-1)=0 equation:


Simplifying
(2 + w)(5w + -1) = 0

Reorder the terms:
(2 + w)(-1 + 5w) = 0

Multiply (2 + w) * (-1 + 5w)
(2(-1 + 5w) + w(-1 + 5w)) = 0
((-1 * 2 + 5w * 2) + w(-1 + 5w)) = 0
((-2 + 10w) + w(-1 + 5w)) = 0
(-2 + 10w + (-1 * w + 5w * w)) = 0
(-2 + 10w + (-1w + 5w2)) = 0

Combine like terms: 10w + -1w = 9w
(-2 + 9w + 5w2) = 0

Solving
-2 + 9w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2 + -1w)(1 + -5w) = 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 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 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 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2

Solution

w = {-2, 0.2}

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