(3w-7)(5+w)=0

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Solution for (3w-7)(5+w)=0 equation: 


Simplifying
(3w + -7)(5 + w) = 0

Reorder the terms:
(-7 + 3w)(5 + w) = 0

Multiply (-7 + 3w) * (5 + w)
(-7(5 + w) + 3w * (5 + w)) = 0
((5 * -7 + w * -7) + 3w * (5 + w)) = 0
((-35 + -7w) + 3w * (5 + w)) = 0
(-35 + -7w + (5 * 3w + w * 3w)) = 0
(-35 + -7w + (15w + 3w2)) = 0

Combine like terms: -7w + 15w = 8w
(-35 + 8w + 3w2) = 0

Solving
-35 + 8w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -1w)(7 + -3w) = 0


Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve:

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 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 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5

Subproblem 2
Set the factor '(7 + -3w)' equal to zero and attempt to solve:

Simplifying
7 + -3w = 0

Solving
7 + -3w = 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 + -3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3w = 0 + -7
-3w = 0 + -7

Combine like terms: 0 + -7 = -7
-3w = -7

Divide each side by '-3'.
w = 2.333333333

Simplifying
w = 2.333333333
Solution
w = {-5, 2.333333333}

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