(a+1)(a-5)=7

Solution for (a+1)(a-5)=7 equation:

Simplifying
(a + 1)(a + -5) = 7

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

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

Multiply (1 + a) * (-5 + a)
(1(-5 + a) + a(-5 + a)) = 7
((-5 * 1 + a * 1) + a(-5 + a)) = 7
((-5 + 1a) + a(-5 + a)) = 7
(-5 + 1a + (-5 * a + a * a)) = 7
(-5 + 1a + (-5a + a2)) = 7

Combine like terms: 1a + -5a = -4a
(-5 + -4a + a2) = 7

Solving
-5 + -4a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
-5 + -7 + -4a + a2 = 7 + -7

Combine like terms: -5 + -7 = -12
-12 + -4a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-12 + -4a + a2 = 0

Factor a trinomial.
(-2 + -1a)(6 + -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 '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-2, 6}