5(w+7)*4(w+5)=

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Solution for 5(w+7)*4(w+5)= equation: 


Simplifying
5(w + 7) * 4(w + 5) = 0

Reorder the terms:
5(7 + w) * 4(w + 5) = 0

Reorder the terms:
5(7 + w) * 4(5 + w) = 0

Reorder the terms for easier multiplication:
5 * 4(7 + w)(5 + w) = 0

Multiply 5 * 4
20(7 + w)(5 + w) = 0

Multiply (7 + w) * (5 + w)
20(7(5 + w) + w(5 + w)) = 0
20((5 * 7 + w * 7) + w(5 + w)) = 0
20((35 + 7w) + w(5 + w)) = 0
20(35 + 7w + (5 * w + w * w)) = 0
20(35 + 7w + (5w + w2)) = 0

Combine like terms: 7w + 5w = 12w
20(35 + 12w + w2) = 0
(35 * 20 + 12w * 20 + w2 * 20) = 0
(700 + 240w + 20w2) = 0

Solving
700 + 240w + 20w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '20'.
20(35 + 12w + w2) = 0

Factor a trinomial.
20((7 + w)(5 + w)) = 0

Ignore the factor 20.

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 '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {-7, -5}

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