d^2+d-5=1

Solution for d^2+d-5=1 equation:

Simplifying
d2 + d + -5 = 1

Reorder the terms:
-5 + d + d2 = 1

Solving
-5 + d + d2 = 1

Solving for variable 'd'.

Reorder the terms:
-5 + -1 + d + d2 = 1 + -1

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

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

Factor a trinomial.
(-3 + -1d)(2 + -1d) = 0

Subproblem 1
Set the factor '(-3 + -1d)' equal to zero and attempt to solve:

Simplifying
-3 + -1d = 0

Solving
-3 + -1d = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1d = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1d = 0 + 3
-1d = 0 + 3

Combine like terms: 0 + 3 = 3
-1d = 3

Divide each side by '-1'.
d = -3

Simplifying
d = -3
Subproblem 2
Set the factor '(2 + -1d)' equal to zero and attempt to solve:

Simplifying
2 + -1d = 0

Solving
2 + -1d = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1d = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1d = 0 + -2
-1d = 0 + -2

Combine like terms: 0 + -2 = -2
-1d = -2

Divide each side by '-1'.
d = 2

Simplifying
d = 2
Solution
d = {-3, 2}