(z+1)(z-4)=0

Solution for (z+1)(z-4)=0 equation:

Simplifying
(z + 1)(z + -4) = 0

Reorder the terms:
(1 + z)(z + -4) = 0

Reorder the terms:
(1 + z)(-4 + z) = 0

Multiply (1 + z) * (-4 + z)
(1(-4 + z) + z(-4 + z)) = 0
((-4 * 1 + z * 1) + z(-4 + z)) = 0
((-4 + 1z) + z(-4 + z)) = 0
(-4 + 1z + (-4 * z + z * z)) = 0
(-4 + 1z + (-4z + z2)) = 0

Combine like terms: 1z + -4z = -3z
(-4 + -3z + z2) = 0

Solving
-4 + -3z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(4 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-1, 4}