(a+4)(a-6)=-21

Solution for (a+4)(a-6)=-21 equation:

Simplifying
(a + 4)(a + -6) = -21

Reorder the terms:
(4 + a)(a + -6) = -21

Reorder the terms:
(4 + a)(-6 + a) = -21

Multiply (4 + a) * (-6 + a)
(4(-6 + a) + a(-6 + a)) = -21
((-6 * 4 + a * 4) + a(-6 + a)) = -21
((-24 + 4a) + a(-6 + a)) = -21
(-24 + 4a + (-6 * a + a * a)) = -21
(-24 + 4a + (-6a + a2)) = -21

Combine like terms: 4a + -6a = -2a
(-24 + -2a + a2) = -21

Solving
-24 + -2a + a2 = -21

Solving for variable 'a'.

Reorder the terms:
-24 + 21 + -2a + a2 = -21 + 21

Combine like terms: -24 + 21 = -3
-3 + -2a + a2 = -21 + 21

Combine like terms: -21 + 21 = 0
-3 + -2a + a2 = 0

Factor a trinomial.
(-1 + -1a)(3 + -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 '(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
Solution
a = {-1, 3}