3y^2+46y-32=0

Solution for 3y^2+46y-32=0 equation:

Simplifying
3y2 + 46y + -32 = 0

Reorder the terms:
-32 + 46y + 3y2 = 0

Solving
-32 + 46y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-16 + -1y)(2 + -3y) = 0

Subproblem 1
Set the factor '(-16 + -1y)' equal to zero and attempt to solve:

Simplifying
-16 + -1y = 0

Solving
-16 + -1y = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1y = 0 + 16
-1y = 0 + 16

Combine like terms: 0 + 16 = 16
-1y = 16

Divide each side by '-1'.
y = -16

Simplifying
y = -16
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 = {-16, 0.6666666667}