3y^2=10y-3

Solution for 3y^2=10y-3 equation:

Simplifying
3y2 = 10y + -3

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

Solving
3y2 = -3 + 10y

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {0.3333333333, 3}