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

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

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

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

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

Multiply (5 + 3w) * (3 + w)
(5(3 + w) + 3w * (3 + w)) = 7
((3 * 5 + w * 5) + 3w * (3 + w)) = 7
((15 + 5w) + 3w * (3 + w)) = 7
(15 + 5w + (3 * 3w + w * 3w)) = 7
(15 + 5w + (9w + 3w2)) = 7

Combine like terms: 5w + 9w = 14w
(15 + 14w + 3w2) = 7

Solving
15 + 14w + 3w2 = 7

Solving for variable 'w'.

Reorder the terms:
15 + -7 + 14w + 3w2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14w + 3w2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14w + 3w2 = 0

Factor a trinomial.
(4 + w)(2 + 3w) = 0

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 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 + w = 0 + -4

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

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

Simplifying
w = -4
Subproblem 2
Set the factor '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 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 + 3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3w = 0 + -2
3w = 0 + -2

Combine like terms: 0 + -2 = -2
3w = -2

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {-4, -0.6666666667}