(z+4)(z-2)=-5

Solution for (z+4)(z-2)=-5 equation:

Simplifying
(z + 4)(z + -2) = -5

Reorder the terms:
(4 + z)(z + -2) = -5

Reorder the terms:
(4 + z)(-2 + z) = -5

Multiply (4 + z) * (-2 + z)
(4(-2 + z) + z(-2 + z)) = -5
((-2 * 4 + z * 4) + z(-2 + z)) = -5
((-8 + 4z) + z(-2 + z)) = -5
(-8 + 4z + (-2 * z + z * z)) = -5
(-8 + 4z + (-2z + z2)) = -5

Combine like terms: 4z + -2z = 2z
(-8 + 2z + z2) = -5

Solving
-8 + 2z + z2 = -5

Solving for variable 'z'.

Reorder the terms:
-8 + 5 + 2z + z2 = -5 + 5

Combine like terms: -8 + 5 = -3
-3 + 2z + z2 = -5 + 5

Combine like terms: -5 + 5 = 0
-3 + 2z + z2 = 0

Factor a trinomial.
(-3 + -1z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {-3, 1}