(a-3)(a+7)=-9

Solution for (a-3)(a+7)=-9 equation:

Simplifying
(a + -3)(a + 7) = -9

Reorder the terms:
(-3 + a)(a + 7) = -9

Reorder the terms:
(-3 + a)(7 + a) = -9

Multiply (-3 + a) * (7 + a)
(-3(7 + a) + a(7 + a)) = -9
((7 * -3 + a * -3) + a(7 + a)) = -9
((-21 + -3a) + a(7 + a)) = -9
(-21 + -3a + (7 * a + a * a)) = -9
(-21 + -3a + (7a + a2)) = -9

Combine like terms: -3a + 7a = 4a
(-21 + 4a + a2) = -9

Solving
-21 + 4a + a2 = -9

Solving for variable 'a'.

Reorder the terms:
-21 + 9 + 4a + a2 = -9 + 9

Combine like terms: -21 + 9 = -12
-12 + 4a + a2 = -9 + 9

Combine like terms: -9 + 9 = 0
-12 + 4a + a2 = 0

Factor a trinomial.
(-6 + -1a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

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

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

Divide each side by '-1'.
a = -6

Simplifying
a = -6
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 = {-6, 2}