(5w+1)(7+w)=0

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Solution for (5w+1)(7+w)=0 equation: 


Simplifying
(5w + 1)(7 + w) = 0

Reorder the terms:
(1 + 5w)(7 + w) = 0

Multiply (1 + 5w) * (7 + w)
(1(7 + w) + 5w * (7 + w)) = 0
((7 * 1 + w * 1) + 5w * (7 + w)) = 0
((7 + 1w) + 5w * (7 + w)) = 0
(7 + 1w + (7 * 5w + w * 5w)) = 0
(7 + 1w + (35w + 5w2)) = 0

Combine like terms: 1w + 35w = 36w
(7 + 36w + 5w2) = 0

Solving
7 + 36w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + w)(1 + 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 '(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 = {-7, -0.2}

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