6d^2+21d=10d+35

Solution for 6d^2+21d=10d+35 equation:

Simplifying
6d2 + 21d = 10d + 35

Reorder the terms:
21d + 6d2 = 10d + 35

Reorder the terms:
21d + 6d2 = 35 + 10d

Solving
21d + 6d2 = 35 + 10d

Solving for variable 'd'.

Reorder the terms:
-35 + 21d + -10d + 6d2 = 35 + 10d + -35 + -10d

Combine like terms: 21d + -10d = 11d
-35 + 11d + 6d2 = 35 + 10d + -35 + -10d

Reorder the terms:
-35 + 11d + 6d2 = 35 + -35 + 10d + -10d

Combine like terms: 35 + -35 = 0
-35 + 11d + 6d2 = 0 + 10d + -10d
-35 + 11d + 6d2 = 10d + -10d

Combine like terms: 10d + -10d = 0
-35 + 11d + 6d2 = 0

Factor a trinomial.
(-7 + -2d)(5 + -3d) = 0

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

Simplifying
-7 + -2d = 0

Solving
-7 + -2d = 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 + -2d = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2d = 0 + 7
-2d = 0 + 7

Combine like terms: 0 + 7 = 7
-2d = 7

Divide each side by '-2'.
d = -3.5

Simplifying
d = -3.5
Subproblem 2
Set the factor '(5 + -3d)' equal to zero and attempt to solve:

Simplifying
5 + -3d = 0

Solving
5 + -3d = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3d = 0 + -5
-3d = 0 + -5

Combine like terms: 0 + -5 = -5
-3d = -5

Divide each side by '-3'.
d = 1.666666667

Simplifying
d = 1.666666667
Solution
d = {-3.5, 1.666666667}