(a-5)(a+3)=-7

Solution for (a-5)(a+3)=-7 equation:

Simplifying
(a + -5)(a + 3) = -7

Reorder the terms:
(-5 + a)(a + 3) = -7

Reorder the terms:
(-5 + a)(3 + a) = -7

Multiply (-5 + a) * (3 + a)
(-5(3 + a) + a(3 + a)) = -7
((3 * -5 + a * -5) + a(3 + a)) = -7
((-15 + -5a) + a(3 + a)) = -7
(-15 + -5a + (3 * a + a * a)) = -7
(-15 + -5a + (3a + a2)) = -7

Combine like terms: -5a + 3a = -2a
(-15 + -2a + a2) = -7

Solving
-15 + -2a + a2 = -7

Solving for variable 'a'.

Reorder the terms:
-15 + 7 + -2a + a2 = -7 + 7

Combine like terms: -15 + 7 = -8
-8 + -2a + a2 = -7 + 7

Combine like terms: -7 + 7 = 0
-8 + -2a + a2 = 0

Factor a trinomial.
(-2 + -1a)(4 + -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 '(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
Solution
a = {-2, 4}