(a+5)(a-2)=-6

Solution for (a+5)(a-2)=-6 equation:

Simplifying
(a + 5)(a + -2) = -6

Reorder the terms:
(5 + a)(a + -2) = -6

Reorder the terms:
(5 + a)(-2 + a) = -6

Multiply (5 + a) * (-2 + a)
(5(-2 + a) + a(-2 + a)) = -6
((-2 * 5 + a * 5) + a(-2 + a)) = -6
((-10 + 5a) + a(-2 + a)) = -6
(-10 + 5a + (-2 * a + a * a)) = -6
(-10 + 5a + (-2a + a2)) = -6

Combine like terms: 5a + -2a = 3a
(-10 + 3a + a2) = -6

Solving
-10 + 3a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
-10 + 6 + 3a + a2 = -6 + 6

Combine like terms: -10 + 6 = -4
-4 + 3a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
-4 + 3a + a2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-4, 1}