(a+2)(a-1)-4=0

Solution for (a+2)(a-1)-4=0 equation:

Simplifying
(a + 2)(a + -1) + -4 = 0

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

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

Multiply (2 + a) * (-1 + a)
(2(-1 + a) + a(-1 + a)) + -4 = 0
((-1 * 2 + a * 2) + a(-1 + a)) + -4 = 0
((-2 + 2a) + a(-1 + a)) + -4 = 0
(-2 + 2a + (-1 * a + a * a)) + -4 = 0
(-2 + 2a + (-1a + a2)) + -4 = 0

Combine like terms: 2a + -1a = 1a
(-2 + 1a + a2) + -4 = 0

Reorder the terms:
-2 + -4 + 1a + a2 = 0

Combine like terms: -2 + -4 = -6
-6 + 1a + a2 = 0

Solving
-6 + 1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(2 + -1a) = 0

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

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

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

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

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

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-3, 2}