6d^2+2d-27=1

Solution for 6d^2+2d-27=1 equation:

Simplifying
6d2 + 2d + -27 = 1

Reorder the terms:
-27 + 2d + 6d2 = 1

Solving
-27 + 2d + 6d2 = 1

Solving for variable 'd'.

Reorder the terms:
-27 + -1 + 2d + 6d2 = 1 + -1

Combine like terms: -27 + -1 = -28
-28 + 2d + 6d2 = 1 + -1

Combine like terms: 1 + -1 = 0
-28 + 2d + 6d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + d + 3d2) = 0

Factor a trinomial.
2((-7 + -3d)(2 + -1d)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -3d)' equal to zero and attempt to solve:

Simplifying
-7 + -3d = 0

Solving
-7 + -3d = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3d = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3d = 0 + 7
-3d = 0 + 7

Combine like terms: 0 + 7 = 7
-3d = 7

Divide each side by '-3'.
d = -2.333333333

Simplifying
d = -2.333333333
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 = {-2.333333333, 2}