(5+z)(5z+2)=0

Solution for (5+z)(5z+2)=0 equation:

Simplifying
(5 + z)(5z + 2) = 0

Reorder the terms:
(5 + z)(2 + 5z) = 0

Multiply (5 + z) * (2 + 5z)
(5(2 + 5z) + z(2 + 5z)) = 0
((2 * 5 + 5z * 5) + z(2 + 5z)) = 0
((10 + 25z) + z(2 + 5z)) = 0
(10 + 25z + (2 * z + 5z * z)) = 0
(10 + 25z + (2z + 5z2)) = 0

Combine like terms: 25z + 2z = 27z
(10 + 27z + 5z2) = 0

Solving
10 + 27z + 5z2 = 0

Solving for variable 'z'.

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

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

Simplifying
5 + z = 0

Solving
5 + z = 0

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

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

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

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

Simplifying
z = -5
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 = {-5, -0.4}