(1+z)(5z+6)=0

Solution for (1+z)(5z+6)=0 equation:

Simplifying
(1 + z)(5z + 6) = 0

Reorder the terms:
(1 + z)(6 + 5z) = 0

Multiply (1 + z) * (6 + 5z)
(1(6 + 5z) + z(6 + 5z)) = 0
((6 * 1 + 5z * 1) + z(6 + 5z)) = 0
((6 + 5z) + z(6 + 5z)) = 0
(6 + 5z + (6 * z + 5z * z)) = 0
(6 + 5z + (6z + 5z2)) = 0

Combine like terms: 5z + 6z = 11z
(6 + 11z + 5z2) = 0

Solving
6 + 11z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + 5z)(1 + z) = 0

Subproblem 1
Set the factor '(6 + 5z)' equal to zero and attempt to solve:

Simplifying
6 + 5z = 0

Solving
6 + 5z = 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 + 5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5z = 0 + -6
5z = 0 + -6

Combine like terms: 0 + -6 = -6
5z = -6

Divide each side by '5'.
z = -1.2

Simplifying
z = -1.2
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

Add '-1' to each side of the equation.
1 + -1 + z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z = 0 + -1
z = 0 + -1

Combine like terms: 0 + -1 = -1
z = -1

Simplifying
z = -1
Solution
z = {-1.2, -1}