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

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

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

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

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

Multiply (5 + z) * (-6 + z)
(5(-6 + z) + z(-6 + z)) = 0
((-6 * 5 + z * 5) + z(-6 + z)) = 0
((-30 + 5z) + z(-6 + z)) = 0
(-30 + 5z + (-6 * z + z * z)) = 0
(-30 + 5z + (-6z + z2)) = 0

Combine like terms: 5z + -6z = -1z
(-30 + -1z + z2) = 0

Solving
-30 + -1z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-5, 6}