(5z+7)(z+5)=23

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

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

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

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

Multiply (7 + 5z) * (5 + z)
(7(5 + z) + 5z * (5 + z)) = 23
((5 * 7 + z * 7) + 5z * (5 + z)) = 23
((35 + 7z) + 5z * (5 + z)) = 23
(35 + 7z + (5 * 5z + z * 5z)) = 23
(35 + 7z + (25z + 5z2)) = 23

Combine like terms: 7z + 25z = 32z
(35 + 32z + 5z2) = 23

Solving
35 + 32z + 5z2 = 23

Solving for variable 'z'.

Reorder the terms:
35 + -23 + 32z + 5z2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32z + 5z2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32z + 5z2 = 0

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

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

Simplifying
6 + z = 0

Solving
6 + z = 0

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

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

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

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

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

Simplifying
2 + 5z = 0

Solving
2 + 5z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5z = 0 + -2

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

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

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

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