(d-6)(d+1)=0

Solution for (d-6)(d+1)=0 equation:

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

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

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

Multiply (-6 + d) * (1 + d)
(-6(1 + d) + d(1 + d)) = 0
((1 * -6 + d * -6) + d(1 + d)) = 0
((-6 + -6d) + d(1 + d)) = 0
(-6 + -6d + (1 * d + d * d)) = 0
(-6 + -6d + (1d + d2)) = 0

Combine like terms: -6d + 1d = -5d
(-6 + -5d + d2) = 0

Solving
-6 + -5d + d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-1 + -1d)(6 + -1d) = 0

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

Simplifying
-1 + -1d = 0

Solving
-1 + -1d = 0

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

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

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

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

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

Simplifying
d = -1
Subproblem 2
Set the factor '(6 + -1d)' equal to zero and attempt to solve:

Simplifying
6 + -1d = 0

Solving
6 + -1d = 0

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

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

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

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

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

Simplifying
d = 6
Solution
d = {-1, 6}