(3w+4)(7+w)=0

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Solution for (3w+4)(7+w)=0 equation: 


Simplifying
(3w + 4)(7 + w) = 0

Reorder the terms:
(4 + 3w)(7 + w) = 0

Multiply (4 + 3w) * (7 + w)
(4(7 + w) + 3w * (7 + w)) = 0
((7 * 4 + w * 4) + 3w * (7 + w)) = 0
((28 + 4w) + 3w * (7 + w)) = 0
(28 + 4w + (7 * 3w + w * 3w)) = 0
(28 + 4w + (21w + 3w2)) = 0

Combine like terms: 4w + 21w = 25w
(28 + 25w + 3w2) = 0

Solving
28 + 25w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + w)(4 + 3w) = 0


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 '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w = 0 + -4
3w = 0 + -4

Combine like terms: 0 + -4 = -4
3w = -4

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
Solution
w = {-7, -1.333333333}

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