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

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


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

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

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