7d^2+20d-d+40=106

Solution for 7d^2+20d-d+40=106 equation:

Simplifying
7d2 + 20d + -1d + 40 = 106

Reorder the terms:
40 + 20d + -1d + 7d2 = 106

Combine like terms: 20d + -1d = 19d
40 + 19d + 7d2 = 106

Solving
40 + 19d + 7d2 = 106

Solving for variable 'd'.

Reorder the terms:
40 + -106 + 19d + 7d2 = 106 + -106

Combine like terms: 40 + -106 = -66
-66 + 19d + 7d2 = 106 + -106

Combine like terms: 106 + -106 = 0
-66 + 19d + 7d2 = 0

Factor a trinomial.
(-33 + -7d)(2 + -1d) = 0

Subproblem 1
Set the factor '(-33 + -7d)' equal to zero and attempt to solve:

Simplifying
-33 + -7d = 0

Solving
-33 + -7d = 0

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

Add '33' to each side of the equation.
-33 + 33 + -7d = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -7d = 0 + 33
-7d = 0 + 33

Combine like terms: 0 + 33 = 33
-7d = 33

Divide each side by '-7'.
d = -4.714285714

Simplifying
d = -4.714285714
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 = {-4.714285714, 2}