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

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


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

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

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

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

Combine like terms: 5w + 35w = 40w
(35 + 40w + 5w2) = 0

Solving
35 + 40w + 5w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + 8w + w2) = 0

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

Ignore the factor 5.

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 '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1

Solution

w = {-7, -1}

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