3y^2+4y+6=10

Solution for 3y^2+4y+6=10 equation:

Simplifying
3y2 + 4y + 6 = 10

Reorder the terms:
6 + 4y + 3y2 = 10

Solving
6 + 4y + 3y2 = 10

Solving for variable 'y'.

Reorder the terms:
6 + -10 + 4y + 3y2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 4y + 3y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 4y + 3y2 = 0

Factor a trinomial.
(-2 + -1y)(2 + -3y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
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
Solution
y = {-2, 0.6666666667}