(a-12)(a+1)=-40

Solution for (a-12)(a+1)=-40 equation:

Simplifying
(a + -12)(a + 1) = -40

Reorder the terms:
(-12 + a)(a + 1) = -40

Reorder the terms:
(-12 + a)(1 + a) = -40

Multiply (-12 + a) * (1 + a)
(-12(1 + a) + a(1 + a)) = -40
((1 * -12 + a * -12) + a(1 + a)) = -40
((-12 + -12a) + a(1 + a)) = -40
(-12 + -12a + (1 * a + a * a)) = -40
(-12 + -12a + (1a + a2)) = -40

Combine like terms: -12a + 1a = -11a
(-12 + -11a + a2) = -40

Solving
-12 + -11a + a2 = -40

Solving for variable 'a'.

Reorder the terms:
-12 + 40 + -11a + a2 = -40 + 40

Combine like terms: -12 + 40 = 28
28 + -11a + a2 = -40 + 40

Combine like terms: -40 + 40 = 0
28 + -11a + a2 = 0

Factor a trinomial.
(4 + -1a)(7 + -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 '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {4, 7}