(5w+7)(w+5)=23

Solution for (5w+7)(w+5)=23 equation:

Simplifying
(5w + 7)(w + 5) = 23

Reorder the terms:
(7 + 5w)(w + 5) = 23

Reorder the terms:
(7 + 5w)(5 + w) = 23

Multiply (7 + 5w) * (5 + w)
(7(5 + w) + 5w * (5 + w)) = 23
((5 * 7 + w * 7) + 5w * (5 + w)) = 23
((35 + 7w) + 5w * (5 + w)) = 23
(35 + 7w + (5 * 5w + w * 5w)) = 23
(35 + 7w + (25w + 5w2)) = 23

Combine like terms: 7w + 25w = 32w
(35 + 32w + 5w2) = 23

Solving
35 + 32w + 5w2 = 23

Solving for variable 'w'.

Reorder the terms:
35 + -23 + 32w + 5w2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32w + 5w2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32w + 5w2 = 0

Factor a trinomial.
(6 + w)(2 + 5w) = 0

Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(2 + 5w)' equal to zero and attempt to solve:

Simplifying
2 + 5w = 0

Solving
2 + 5w = 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 + 5w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5w = 0 + -2
5w = 0 + -2

Combine like terms: 0 + -2 = -2
5w = -2

Divide each side by '5'.
w = -0.4

Simplifying
w = -0.4
Solution
w = {-6, -0.4}