3d(4d-10)=1190

Solution for 3d(4d-10)=1190 equation:

Simplifying
3d(4d + -10) = 1190

Reorder the terms:
3d(-10 + 4d) = 1190
(-10 * 3d + 4d * 3d) = 1190
(-30d + 12d2) = 1190

Solving
-30d + 12d2 = 1190

Solving for variable 'd'.

Reorder the terms:
-1190 + -30d + 12d2 = 1190 + -1190

Combine like terms: 1190 + -1190 = 0
-1190 + -30d + 12d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-595 + -15d + 6d2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-595 + -15d + 6d2)' equal to zero and attempt to solve:

Simplifying
-595 + -15d + 6d2 = 0

Solving
-595 + -15d + 6d2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-99.16666667 + -2.5d + d2 = 0

Move the constant term to the right:

Add '99.16666667' to each side of the equation.
-99.16666667 + -2.5d + 99.16666667 + d2 = 0 + 99.16666667

Reorder the terms:
-99.16666667 + 99.16666667 + -2.5d + d2 = 0 + 99.16666667

Combine like terms: -99.16666667 + 99.16666667 = 0.00000000
0.00000000 + -2.5d + d2 = 0 + 99.16666667
-2.5d + d2 = 0 + 99.16666667

Combine like terms: 0 + 99.16666667 = 99.16666667
-2.5d + d2 = 99.16666667

The d term is -2.5d.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5d + 1.5625 + d2 = 99.16666667 + 1.5625

Reorder the terms:
1.5625 + -2.5d + d2 = 99.16666667 + 1.5625

Combine like terms: 99.16666667 + 1.5625 = 100.72916667
1.5625 + -2.5d + d2 = 100.72916667

Factor a perfect square on the left side:
(d + -1.25)(d + -1.25) = 100.72916667

Calculate the square root of the right side: 10.036392114

Break this problem into two subproblems by setting 
(d + -1.25) equal to 10.036392114 and -10.036392114.

Subproblem 1
d + -1.25 = 10.036392114

Simplifying
d + -1.25 = 10.036392114

Reorder the terms:
-1.25 + d = 10.036392114

Solving
-1.25 + d = 10.036392114

Solving for variable 'd'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + d = 10.036392114 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + d = 10.036392114 + 1.25
d = 10.036392114 + 1.25

Combine like terms: 10.036392114 + 1.25 = 11.286392114
d = 11.286392114

Simplifying
d = 11.286392114

Subproblem 2
d + -1.25 = -10.036392114

Simplifying
d + -1.25 = -10.036392114

Reorder the terms:
-1.25 + d = -10.036392114

Solving
-1.25 + d = -10.036392114

Solving for variable 'd'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + d = -10.036392114 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + d = -10.036392114 + 1.25
d = -10.036392114 + 1.25

Combine like terms: -10.036392114 + 1.25 = -8.786392114
d = -8.786392114

Simplifying
d = -8.786392114

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {11.286392114, -8.786392114}
Solution
d = {11.286392114, -8.786392114}