(a+1)(a-6)=

Solution for (a+1)(a-6)= equation:

Simplifying
(a + 1)(a + -6) = 0

Reorder the terms:
(1 + a)(a + -6) = 0

Reorder the terms:
(1 + a)(-6 + a) = 0

Multiply (1 + a) * (-6 + a)
(1(-6 + a) + a(-6 + a)) = 0
((-6 * 1 + a * 1) + a(-6 + a)) = 0
((-6 + 1a) + a(-6 + a)) = 0
(-6 + 1a + (-6 * a + a * a)) = 0
(-6 + 1a + (-6a + a2)) = 0

Combine like terms: 1a + -6a = -5a
(-6 + -5a + a2) = 0

Solving
-6 + -5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1a)(6 + -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 '(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 = {-1, 6}