(a-4)(a+3)=-6

Solution for (a-4)(a+3)=-6 equation:

Simplifying
(a + -4)(a + 3) = -6

Reorder the terms:
(-4 + a)(a + 3) = -6

Reorder the terms:
(-4 + a)(3 + a) = -6

Multiply (-4 + a) * (3 + a)
(-4(3 + a) + a(3 + a)) = -6
((3 * -4 + a * -4) + a(3 + a)) = -6
((-12 + -4a) + a(3 + a)) = -6
(-12 + -4a + (3 * a + a * a)) = -6
(-12 + -4a + (3a + a2)) = -6

Combine like terms: -4a + 3a = -1a
(-12 + -1a + a2) = -6

Solving
-12 + -1a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
-12 + 6 + -1a + a2 = -6 + 6

Combine like terms: -12 + 6 = -6
-6 + -1a + a2 = -6 + 6

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

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

Subproblem 1
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
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 = {-2, 3}