(4w+2)(7-w)=0

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Solution for (4w+2)(7-w)=0 equation: 


Simplifying
(4w + 2)(7 + -1w) = 0

Reorder the terms:
(2 + 4w)(7 + -1w) = 0

Multiply (2 + 4w) * (7 + -1w)
(2(7 + -1w) + 4w * (7 + -1w)) = 0
((7 * 2 + -1w * 2) + 4w * (7 + -1w)) = 0
((14 + -2w) + 4w * (7 + -1w)) = 0
(14 + -2w + (7 * 4w + -1w * 4w)) = 0
(14 + -2w + (28w + -4w2)) = 0

Combine like terms: -2w + 28w = 26w
(14 + 26w + -4w2) = 0

Solving
14 + 26w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 13w + -2w2) = 0

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

Ignore the factor 2.

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

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7

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

Simplifying
1 + 2w = 0

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

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

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

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {7, -0.5}

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