Question

I'll give a medal to whoever helps!
Factor: 2d^2-12d+18

Answer 1

Simplifying
2d2 = 12d + -16

Reorder the terms:
2d2 = -16 + 12d

Solving
2d2 = -16 + 12d

Solving for variable 'd'.

Reorder the terms:
16 + -12d + 2d2 = -16 + 12d + 16 + -12d

Reorder the terms:
16 + -12d + 2d2 = -16 + 16 + 12d + -12d

Combine like terms: -16 + 16 = 0
16 + -12d + 2d2 = 0 + 12d + -12d
16 + -12d + 2d2 = 12d + -12d

Combine like terms: 12d + -12d = 0
16 + -12d + 2d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -6d + d2) = 0

Factor a trinomial.
2((2 + -1d)(4 + -1d)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1d)' equal to zero and attempt to solve:

Simplifying
4 + -1d = 0

Solving
4 + -1d = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1d = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1d = 0 + -4
-1d = 0 + -4

Combine like terms: 0 + -4 = -4
-1d = -4

Divide each side by '-1'.
d = 4

Simplifying
d = 4
Solution
d = {2, 4}.

Answer 2

I hope THAT helps some.

Answer 3

(2d-6)(d-3) if you multiply out =2d^2 -6d-3d+18
so 2d=6 so d=3 or 3