(5w-2)(7+w)=0

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Solution for (5w-2)(7+w)=0 equation:


Simplifying
(5w + -2)(7 + w) = 0

Reorder the terms:
(-2 + 5w)(7 + w) = 0

Multiply (-2 + 5w) * (7 + w)
(-2(7 + w) + 5w * (7 + w)) = 0
((7 * -2 + w * -2) + 5w * (7 + w)) = 0
((-14 + -2w) + 5w * (7 + w)) = 0
(-14 + -2w + (7 * 5w + w * 5w)) = 0
(-14 + -2w + (35w + 5w2)) = 0

Combine like terms: -2w + 35w = 33w
(-14 + 33w + 5w2) = 0

Solving
-14 + 33w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(2 + -5w) = 0

Subproblem 1

Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7

Subproblem 2

Set the factor '(2 + -5w)' equal to zero and attempt to solve: Simplifying 2 + -5w = 0 Solving 2 + -5w = 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 + -5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5w = 0 + -2 -5w = 0 + -2 Combine like terms: 0 + -2 = -2 -5w = -2 Divide each side by '-5'. w = 0.4 Simplifying w = 0.4

Solution

w = {-7, 0.4}

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