6(2y^2+1)=17y

Solution for 6(2y^2+1)=17y equation:

Simplifying
6(2y2 + 1) = 17y

Reorder the terms:
6(1 + 2y2) = 17y
(1 * 6 + 2y2 * 6) = 17y
(6 + 12y2) = 17y

Solving
6 + 12y2 = 17y

Solving for variable 'y'.

Reorder the terms:
6 + -17y + 12y2 = 17y + -17y

Combine like terms: 17y + -17y = 0
6 + -17y + 12y2 = 0

Factor a trinomial.
(2 + -3y)(3 + -4y) = 0

Subproblem 1
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {0.6666666667, 0.75}