(a-7)(a+1)=0

Solution for (a-7)(a+1)=0 equation:

Simplifying
(a + -7)(a + 1) = 0

Reorder the terms:
(-7 + a)(a + 1) = 0

Reorder the terms:
(-7 + a)(1 + a) = 0

Multiply (-7 + a) * (1 + a)
(-7(1 + a) + a(1 + a)) = 0
((1 * -7 + a * -7) + a(1 + a)) = 0
((-7 + -7a) + a(1 + a)) = 0
(-7 + -7a + (1 * a + a * a)) = 0
(-7 + -7a + (1a + a2)) = 0

Combine like terms: -7a + 1a = -6a
(-7 + -6a + a2) = 0

Solving
-7 + -6a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1a)(7 + -1a) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 7}