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

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


Simplifying
(2w + 7)(2 + -1w) = 0

Reorder the terms:
(7 + 2w)(2 + -1w) = 0

Multiply (7 + 2w) * (2 + -1w)
(7(2 + -1w) + 2w * (2 + -1w)) = 0
((2 * 7 + -1w * 7) + 2w * (2 + -1w)) = 0
((14 + -7w) + 2w * (2 + -1w)) = 0
(14 + -7w + (2 * 2w + -1w * 2w)) = 0
(14 + -7w + (4w + -2w2)) = 0

Combine like terms: -7w + 4w = -3w
(14 + -3w + -2w2) = 0

Solving
14 + -3w + -2w2 = 0

Solving for variable 'w'.

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


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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

Subproblem 2
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
Solution
w = {2, -3.5}

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