(a-5)(a+7)=-27

Solution for (a-5)(a+7)=-27 equation:

Simplifying
(a + -5)(a + 7) = -27

Reorder the terms:
(-5 + a)(a + 7) = -27

Reorder the terms:
(-5 + a)(7 + a) = -27

Multiply (-5 + a) * (7 + a)
(-5(7 + a) + a(7 + a)) = -27
((7 * -5 + a * -5) + a(7 + a)) = -27
((-35 + -5a) + a(7 + a)) = -27
(-35 + -5a + (7 * a + a * a)) = -27
(-35 + -5a + (7a + a2)) = -27

Combine like terms: -5a + 7a = 2a
(-35 + 2a + a2) = -27

Solving
-35 + 2a + a2 = -27

Solving for variable 'a'.

Reorder the terms:
-35 + 27 + 2a + a2 = -27 + 27

Combine like terms: -35 + 27 = -8
-8 + 2a + a2 = -27 + 27

Combine like terms: -27 + 27 = 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}