(5w+6)(7+w)=0

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Solution for (5w+6)(7+w)=0 equation:


Simplifying
(5w + 6)(7 + w) = 0

Reorder the terms:
(6 + 5w)(7 + w) = 0

Multiply (6 + 5w) * (7 + w)
(6(7 + w) + 5w * (7 + w)) = 0
((7 * 6 + w * 6) + 5w * (7 + w)) = 0
((42 + 6w) + 5w * (7 + w)) = 0
(42 + 6w + (7 * 5w + w * 5w)) = 0
(42 + 6w + (35w + 5w2)) = 0

Combine like terms: 6w + 35w = 41w
(42 + 41w + 5w2) = 0

Solving
42 + 41w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + w)(6 + 5w) = 0

Subproblem 1

Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7

Subproblem 2

Set the factor '(6 + 5w)' equal to zero and attempt to solve: Simplifying 6 + 5w = 0 Solving 6 + 5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5w = 0 + -6 5w = 0 + -6 Combine like terms: 0 + -6 = -6 5w = -6 Divide each side by '5'. w = -1.2 Simplifying w = -1.2

Solution

w = {-7, -1.2}

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