13y-16=-3y^2

Solution for 13y-16=-3y^2 equation:

Simplifying
13y + -16 = -3y2

Reorder the terms:
-16 + 13y = -3y2

Solving
-16 + 13y = -3y2

Solving for variable 'y'.

Combine like terms: -3y2 + 3y2 = 0
-16 + 13y + 3y2 = 0

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

Subproblem 1
Set the factor '(-16 + -3y)' equal to zero and attempt to solve:

Simplifying
-16 + -3y = 0

Solving
-16 + -3y = 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 + -3y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3y = 0 + 16
-3y = 0 + 16

Combine like terms: 0 + 16 = 16
-3y = 16

Divide each side by '-3'.
y = -5.333333333

Simplifying
y = -5.333333333
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-5.333333333, 1}