(1+w)(5w-8)=0

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Solution for (1+w)(5w-8)=0 equation:


Simplifying
(1 + w)(5w + -8) = 0

Reorder the terms:
(1 + w)(-8 + 5w) = 0

Multiply (1 + w) * (-8 + 5w)
(1(-8 + 5w) + w(-8 + 5w)) = 0
((-8 * 1 + 5w * 1) + w(-8 + 5w)) = 0
((-8 + 5w) + w(-8 + 5w)) = 0
(-8 + 5w + (-8 * w + 5w * w)) = 0
(-8 + 5w + (-8w + 5w2)) = 0

Combine like terms: 5w + -8w = -3w
(-8 + -3w + 5w2) = 0

Solving
-8 + -3w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(8 + -5w) = 0

Subproblem 1

Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 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 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1

Subproblem 2

Set the factor '(8 + -5w)' equal to zero and attempt to solve: Simplifying 8 + -5w = 0 Solving 8 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5w = 0 + -8 -5w = 0 + -8 Combine like terms: 0 + -8 = -8 -5w = -8 Divide each side by '-5'. w = 1.6 Simplifying w = 1.6

Solution

w = {-1, 1.6}

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