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

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

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

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

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

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

Combine like terms: -3a + 5a = 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.
(-4 + -1a)(2 + -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 '(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 = {-4, 2}