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

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


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

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

Multiply (2 + w) * (7 + 2w)
(2(7 + 2w) + w(7 + 2w)) = 0
((7 * 2 + 2w * 2) + w(7 + 2w)) = 0
((14 + 4w) + w(7 + 2w)) = 0
(14 + 4w + (7 * w + 2w * w)) = 0
(14 + 4w + (7w + 2w2)) = 0

Combine like terms: 4w + 7w = 11w
(14 + 11w + 2w2) = 0

Solving
14 + 11w + 2w2 = 0

Solving for variable 'w'.

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


Subproblem 1
Set the factor '(7 + 2w)' equal to zero and attempt to solve:

Simplifying
7 + 2w = 0

Solving
7 + 2w = 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 + 2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2w = 0 + -7
2w = 0 + -7

Combine like terms: 0 + -7 = -7
2w = -7

Divide each side by '2'.
w = -3.5

Simplifying
w = -3.5

Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Solution
w = {-3.5, -2}

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