(a-5)(a+7)=-20

Solution for (a-5)(a+7)=-20 equation:

Simplifying
(a + -5)(a + 7) = -20

Reorder the terms:
(-5 + a)(a + 7) = -20

Reorder the terms:
(-5 + a)(7 + a) = -20

Multiply (-5 + a) * (7 + a)
(-5(7 + a) + a(7 + a)) = -20
((7 * -5 + a * -5) + a(7 + a)) = -20
((-35 + -5a) + a(7 + a)) = -20
(-35 + -5a + (7 * a + a * a)) = -20
(-35 + -5a + (7a + a2)) = -20

Combine like terms: -5a + 7a = 2a
(-35 + 2a + a2) = -20

Solving
-35 + 2a + a2 = -20

Solving for variable 'a'.

Reorder the terms:
-35 + 20 + 2a + a2 = -20 + 20

Combine like terms: -35 + 20 = -15
-15 + 2a + a2 = -20 + 20

Combine like terms: -20 + 20 = 0
-15 + 2a + a2 = 0

Factor a trinomial.
(-5 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
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 = {-5, 3}