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

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

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

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

Multiply (3 + w) * (7 + 5w)
(3(7 + 5w) + w(7 + 5w)) = 0
((7 * 3 + 5w * 3) + w(7 + 5w)) = 0
((21 + 15w) + w(7 + 5w)) = 0
(21 + 15w + (7 * w + 5w * w)) = 0
(21 + 15w + (7w + 5w2)) = 0

Combine like terms: 15w + 7w = 22w
(21 + 22w + 5w2) = 0

Solving
21 + 22w + 5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

Simplifying
w = -3
Subproblem 2
Set the factor '(7 + 5w)' equal to zero and attempt to solve:

Simplifying
7 + 5w = 0

Solving
7 + 5w = 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 + 5w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5w = 0 + -7
5w = 0 + -7

Combine like terms: 0 + -7 = -7
5w = -7

Divide each side by '5'.
w = -1.4

Simplifying
w = -1.4
Solution
w = {-3, -1.4}