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

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

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

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

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

Multiply (1 + a) * (-4 + a)
(1(-4 + a) + a(-4 + a)) = 0
((-4 * 1 + a * 1) + a(-4 + a)) = 0
((-4 + 1a) + a(-4 + a)) = 0
(-4 + 1a + (-4 * a + a * a)) = 0
(-4 + 1a + (-4a + a2)) = 0

Combine like terms: 1a + -4a = -3a
(-4 + -3a + a2) = 0

Solving
-4 + -3a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

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

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

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

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

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

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

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