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

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


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

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

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

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

Combine like terms: -2w + -7w = -9w
-4(-14 + -9w + -1w2) = 0
(-14 * -4 + -9w * -4 + -1w2 * -4) = 0
(56 + 36w + 4w2) = 0

Solving
56 + 36w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + 9w + w2) = 0

Factor a trinomial.
4((7 + w)(2 + w)) = 0

Ignore the factor 4.

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 '(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 = {-7, -2}

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